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

2007/01/29 by Mitsuru Sugimoto, Naohito Tomita, Sugimoto, Mitsuru +1
Mathematics · #42B20 #42B35 #47G30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #math.AP #math.FA #msc:42B20 #msc:42B35 #msc:47G30

paper · pdf · doi:10.48550/arxiv.math/0701832

arxiv created 2007/01/29 · openalex publication_date 2007/01/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 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 Op(S_ρ,δ^m) ⊂ \calL(M^p,q(\Rⁿ)) 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 ≠ 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,δ⁰ with 0<δ<1.

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