Pseudodifferential operators with symbols in the Hörmander class S⁰_α,α on α-modulation spaces

2017/07/31 by Tomoya Kato, Naohito Tomita, Kato, Tomoya +1
Mathematics · #35S05 #42B35 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1707.09710

openalex publication_date 2017/07/31 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the boundedness of pseudodifferential operators with symbols in the Hörmander class S⁰_ρ,ρ on α-modulation spaces M_p,q^s,α, and consider the relation between α and ρ. In particular, we show that pseudodifferential operators with symbols in S⁰_α,α are bounded on all α-modulation spaces M^s,α_p,q, for arbitrary s∈ℝ and for the whole range of exponents 0 < p,q ≤ ∞.

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