We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley g... more We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley g * λ-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BM O functions are also considered.
We give weighted norm inequalities for the maximal fractional operator M q,β of Hardy-Littlewood ... more We give weighted norm inequalities for the maximal fractional operator M q,β of Hardy-Littlewood and the fractional integral I γ. These inequalities are established between (L q , L p) α (X, d, µ) spaces (which are super spaces of Lebesgue spaces L α (X, d, µ), and subspaces of amalgams (L q , L p)(X, d, µ)) and in the setting of space of homogeneous type (X, d, µ). The conditions on the weights are stated in terms of Orlicz norm. Résumé. Nous donnons des inégalitésà poids pour l'opérateur maximal fractionnaire M q,β de Hardy-Littlewood et de l'intégrale fractionnaire I γ. Ces inégalités sontétablies entre des espaces (L q , L p) α (X, d, µ) (qui sont des sur-espaces des espaces de Lebesgue L α (X, d, µ) et des sous-espaces des espaces d'amalgames (L q , L p)(X, d, µ)) et dans le contexte des espaces de type homogènes. Les conditions imposées aux poids sont exprimées en terme de norme d'Orlicz.
Under the assumption that the underlying measure is a non-negative Radon measure which only satis... more Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block H 1 in the sense of distribution, and show that this product may be split into two parts, one in L 1 and the other in some Hardy-Orlicz space.
In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,... more In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,p) and H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞, obtained in our earlier paper [4], we prove that the inclusion of H (1,p) in (L 1 , ℓ p) for 1 ≤ p < ∞ is strict, and more generally, the one of H (q,p) in H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞. Moreover, as other applications, we obtain results of boundedness of Calderón-Zygmund and convolution operators, generalizing those known in the context of the spaces H 1 and BM O(R d).
L'accès aux articles de la revue « Annales mathématiques Blaise Pascal » (http://ambp.cedram.org/... more L'accès aux articles de la revue « Annales mathématiques Blaise Pascal » (http://ambp.cedram.org/), implique l'accord avec les conditions générales d'utilisation (http://ambp.cedram.org/legal/). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm control... more We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm controls of Calderón-Zygmund operators and their associated commutators in the above mention spaces.
It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduc... more It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. Those spaces have a specific dilation behaviour similar to the spaces L α (R d). The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).
In this paper, we carry on with the study of the Hardy-Amalgam spaces H (q,p) loc spaces introduc... more In this paper, we carry on with the study of the Hardy-Amalgam spaces H (q,p) loc spaces introduced in [1]. We investigate their dual spaces and establish some results of boundedness of pseudo-differential operators in these spaces.
We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated t... more We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue qua... more We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces we prove that some classical linear operators such as Calderon–Zygmund, convolution and Riesz potential operators are bounded.
HAL (Le Centre pour la Communication Scientifique Directe), Jan 14, 2016
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. The... more We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. These results allow us to obtain the boundedness of Dunkl-type fractional integral and fractional maximal operators in the Dunkl-Fofana spaces.
We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and ... more We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.
We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated t... more We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.
We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and ... more We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.
In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,... more In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,p) and H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞, obtained in our earlier paper [4], we prove that the inclusion of H (1,p) in (L 1 , ℓ p) for 1 ≤ p < ∞ is strict, and more generally, the one of H (q,p) in H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞. Moreover, as other applications, we obtain results of boundedness of Calderón-Zygmund and convolution operators, generalizing those known in the context of the spaces H 1 and BM O(R d).
Under the assumption that the underlying measure is a non-negative Radon measure which only satis... more Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block ^̋1 in the sense of distribution, and show that this product may be split into two parts, one in L^1 and the other in some Hardy-Orlicz space.
We give an extension to certain RD-space , i.e space of homogeneous type in the sense of Coifman ... more We give an extension to certain RD-space , i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in () and ^̋1(), and functions in Lipschitz space Λ_1/p-1() and ^̋p() for p∈(/+θ,1], where and θ denote respectively the "dimension" and the order of
We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley g... more We prove that the intrinsic square functions including Lusin area integral and Littlewood-Paley g * λ-function as defined by Wilson, are bounded in a class of function spaces include weighted Morrey spaces. The corresponding commutators generated by BM O functions are also considered.
We give weighted norm inequalities for the maximal fractional operator M q,β of Hardy-Littlewood ... more We give weighted norm inequalities for the maximal fractional operator M q,β of Hardy-Littlewood and the fractional integral I γ. These inequalities are established between (L q , L p) α (X, d, µ) spaces (which are super spaces of Lebesgue spaces L α (X, d, µ), and subspaces of amalgams (L q , L p)(X, d, µ)) and in the setting of space of homogeneous type (X, d, µ). The conditions on the weights are stated in terms of Orlicz norm. Résumé. Nous donnons des inégalitésà poids pour l'opérateur maximal fractionnaire M q,β de Hardy-Littlewood et de l'intégrale fractionnaire I γ. Ces inégalités sontétablies entre des espaces (L q , L p) α (X, d, µ) (qui sont des sur-espaces des espaces de Lebesgue L α (X, d, µ) et des sous-espaces des espaces d'amalgames (L q , L p)(X, d, µ)) et dans le contexte des espaces de type homogènes. Les conditions imposées aux poids sont exprimées en terme de norme d'Orlicz.
Under the assumption that the underlying measure is a non-negative Radon measure which only satis... more Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block H 1 in the sense of distribution, and show that this product may be split into two parts, one in L 1 and the other in some Hardy-Orlicz space.
In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,... more In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,p) and H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞, obtained in our earlier paper [4], we prove that the inclusion of H (1,p) in (L 1 , ℓ p) for 1 ≤ p < ∞ is strict, and more generally, the one of H (q,p) in H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞. Moreover, as other applications, we obtain results of boundedness of Calderón-Zygmund and convolution operators, generalizing those known in the context of the spaces H 1 and BM O(R d).
L'accès aux articles de la revue « Annales mathématiques Blaise Pascal » (http://ambp.cedram.org/... more L'accès aux articles de la revue « Annales mathématiques Blaise Pascal » (http://ambp.cedram.org/), implique l'accord avec les conditions générales d'utilisation (http://ambp.cedram.org/legal/). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm control... more We use a molecular characterization of generalized Hardy-Morrey spaces, to provide a norm controls of Calderón-Zygmund operators and their associated commutators in the above mention spaces.
It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduc... more It is the purpose of this paper to give a characterization of the pre-dual of the spaces introduced by I. Fofana on the basis of Wiener amalgam spaces. Those spaces have a specific dilation behaviour similar to the spaces L α (R d). The characterization of the pre-dual will be based on the idea of minimal invariant spaces (with respect to such a group of dilation operators).
In this paper, we carry on with the study of the Hardy-Amalgam spaces H (q,p) loc spaces introduc... more In this paper, we carry on with the study of the Hardy-Amalgam spaces H (q,p) loc spaces introduced in [1]. We investigate their dual spaces and establish some results of boundedness of pseudo-differential operators in these spaces.
We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated t... more We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue qua... more We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces we prove that some classical linear operators such as Calderon–Zygmund, convolution and Riesz potential operators are bounded.
HAL (Le Centre pour la Communication Scientifique Directe), Jan 14, 2016
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. The... more We establish some new properties of the Dunkl-Wiener amalgam spaces defined on the real line. These results allow us to obtain the boundedness of Dunkl-type fractional integral and fractional maximal operators in the Dunkl-Fofana spaces.
We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and ... more We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.
We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated t... more We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.
We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and ... more We generalize Wiener amalgam spaces by using Dunkl translation instead of the classical one, and we give some relationship between these spaces, Dunkl-Lebesgue spaces and Dunkl-Morrey spaces. We prove that the Hardy-Litlewood maximal function associated with the Dunkl operators is bounded on these generalized Dunkl-Morrey spaces.
In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,... more In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces H (q,p) and H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞, obtained in our earlier paper [4], we prove that the inclusion of H (1,p) in (L 1 , ℓ p) for 1 ≤ p < ∞ is strict, and more generally, the one of H (q,p) in H (q,p) loc for 0 < q ≤ 1 and q ≤ p < ∞. Moreover, as other applications, we obtain results of boundedness of Calderón-Zygmund and convolution operators, generalizing those known in the context of the spaces H 1 and BM O(R d).
Under the assumption that the underlying measure is a non-negative Radon measure which only satis... more Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block ^̋1 in the sense of distribution, and show that this product may be split into two parts, one in L^1 and the other in some Hardy-Orlicz space.
We give an extension to certain RD-space , i.e space of homogeneous type in the sense of Coifman ... more We give an extension to certain RD-space , i.e space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in () and ^̋1(), and functions in Lipschitz space Λ_1/p-1() and ^̋p() for p∈(/+θ,1], where and θ denote respectively the "dimension" and the order of
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