Boundedness properties of pseudo-differential operators and Calderón-Zygmund operators on modulation spaces

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dc.creatorSugimoto, Mitsuru
dc.creatorTomita, Naohito
dc.date2007-01-29
dc.date.accessioned2026-07-07T07:43:38Z
dc.date.available2026-07-07T07:43:38Z
dc.descriptionIn this paper, we study the boundedness of pseudo-differential operators with symbols in $S_{ρ,δ}^m$ on the modulation spaces $M^{p,q}$. We discuss the order $m$ for the boundedness $\mathrm{Op}(S_{ρ,δ}^m) \subset \calL(M^{p,q}(\R^n))$ to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space $M^{p,q}$ with $q \neq 2$. This unboundedness is still true even if we assume a generalized T(1) condition. These results are induced by the unboundedness of pseudo-differential operators on $M^{p,q}$ whose symbols are of the class $S_{1,δ}^0$ with $0<δ<1$.
dc.identifierhttps://arxiv.org/abs/math/0701832
dc.identifierhttp://arxiv.org/abs/math/0701832
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122903
dc.subjectFunctional Analysis
dc.subjectAnalysis of PDEs
dc.subject42B20; 42B35; 47G30
dc.titleBoundedness properties of pseudo-differential operators and Calderón-Zygmund operators on modulation spaces
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