A class of Fourier multipliers for modulation spaces

Bényi, Árpád; Grafakos, Loukas; Gröchenig, Karlheinz; Okoudjou, Kasso A.

doi:10.1016/j.acha.2005.02.002

Cited by 36 publications

(41 citation statements)

References 17 publications

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“…The results of this paper were in part inspired by earlier work of three of the authors and Loukas Grafakos [3], in which an analogue of the classical Marcinkiewicz multiplier theorem was proven in the modulation space context. By an easy tensor product argument, the proof of Theorem 1 of [3] (see also [8,Corollary 19]) may be extended to show the following.…”

Section: Abstract Multiplier Theorems On Modulation Spacesmentioning

confidence: 87%

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Unimodular Fourier multipliers for modulation spaces

Bényi

Gröchenig

Okoudjou

et al. 2007

Journal of Functional Analysis

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307

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We investigate the boundedness of unimodular Fourier multipliers on modulation spaces. Surprisingly, the multipliers with general symbol e i|ξ | α , where α ∈ [0, 2], are bounded on all modulation spaces, but, in general, fail to be bounded on the usual L p -spaces. As a consequence, the phase-space concentration of the solutions to the free Schrödinger and wave equations are preserved. As a byproduct, we also obtain boundedness results on modulation spaces for singular multipliers |ξ | −δ sin(|ξ | α ) for 0 δ α.

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Section: Abstract Multiplier Theorems On Modulation Spacesmentioning

confidence: 87%

“…By an easy tensor product argument, the proof of Theorem 1 of [3] (see also [8,Corollary 19]) may be extended to show the following.…”

Section: Abstract Multiplier Theorems On Modulation Spacesmentioning

confidence: 98%

Unimodular Fourier multipliers for modulation spaces

Bényi

Gröchenig

Okoudjou

et al. 2007

Journal of Functional Analysis

Self Cite

203

307

View full text Add to dashboard Cite

show abstract

“…The following result is an immediate consequence of (3.2). On the other hand, [8,Proposition 3.6] and [1]). …”

Section: Remark 46mentioning

confidence: 96%

Changes of variables in modulation and Wiener amalgam spaces

et al. 2011

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In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling–Helson type theorems. We also establish a number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on equation image. Finally, counterparts of these results are discussed for spaces on the torus

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“…The theory of fractional integral operators was studied by many authors (for example, Nakai [6] and Stein [7,Chapter 5]). The theory of modulation spaces was studied by, for example, Bényi, Grafakos, Gröchenig and Okoudjou [1], Feichtinger, Gröchenig and Walnut [2], Tachizawa [8] and Triebel [10]. It is known that modulation spaces are Banach spaces which contain the Sobolev spaces ([4, Proposition 11.3.1]).…”

Section: Introductionmentioning

confidence: 99%