Kasso Okoudjou
University of Maryland, Mathematics, Faculty Member
... 1, 77–91. 5. A class of Fourier multipliers for modulation spaces (with A. Bény, L. Grafakos and K. Gröchenig), Appl. Comput. Harmon. ... Christina Frederick, undergraduate student, working with me through the LSAMP pro-gram (2007 −... more
... 1, 77–91. 5. A class of Fourier multipliers for modulation spaces (with A. Bény, L. Grafakos and K. Gröchenig), Appl. Comput. Harmon. ... Christina Frederick, undergraduate student, working with me through the LSAMP pro-gram (2007 − 2008), and as a Sweet Fellow for NWC. ...
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We show that multilinear pseudodifferential operators with symbols in the modulation space $M^{\infty,1}$ are bounded on products of modulation spaces. In particular, $M^{\infty,1}$ includes non-smooth symbols. Several multilinear... more
We show that multilinear pseudodifferential operators with symbols in the modulation space $M^{\infty,1}$ are bounded on products of modulation spaces. In particular, $M^{\infty,1}$ includes non-smooth symbols. Several multilinear Calder\'on--Vaillancourt-type theorems are then obtained by using certain embeddings of classical function spaces into modulation spaces.
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We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol ei| | , where 2 (0,2), are bounded on all modulation spaces, but, in general, fail to be bounded on... more
We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol ei| | , where 2 (0,2), are bounded on all modulation spaces, but, in general, fail to be bounded on the usual Lp-spaces. As a consequence, the phase-space concentration of the solutions to the free Schrodinger and wave equations are preserved. As a
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Gabor frames fe2inxg(x k)gn;k2Zd provide series representations not only of functions in L2(Rd) but of the entire range of spaces M p;q known as the modulation spaces. Membership of a function or distribution f in the modulation space is... more
Gabor frames fe2inxg(x k)gn;k2Zd provide series representations not only of functions in L2(Rd) but of the entire range of spaces M p;q known as the modulation spaces. Membership of a function or distribution f in the modulation space is characterized by a sequence-space norm of the Gabor coecients of f depending only on the magnitudes of those coecients, and the Gabor series representation of f converges unconditionally in the norm of the mod- ulation space. This paper shows that Gabor expansions also converge in the entire range of amalgam spaces W(Lp;L q), which are not modulation spaces in general but, along with the modulation spaces, play important roles in time-frequency analysis and sampling theory. It is shown that membership of a function or distribution in the amalgam space is characterized by an appropriate sequence space norm of the Gabor coecients. However, this sequence space norm depends on the phase of the Gabor coecients as well as their magnitudes, and the Ga- bor...