Pseudodifferential operators on Mixed-Norm α-modulation spaces

2022/03/29 by Nielsen, Morten
#46E35 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47G30 #Secondary 47B38

paper · doi:10.48550/arxiv.2203.15303

Abstract

Mixed-norm α-modulation spaces were introduced recently by Cleanthous and Georgiadis [Trans. Amer. Math. Soc. 373 (2020), no. 5, 3323-3356]. The mixed-norm spaces M^s,α_p,q(ℝⁿ), α∈ [0,1], form a family of smoothness spaces that contain the mixed-norm Besov spaces as special cases. In this paper we prove that a pseudodifferential operator σ(x,D) with symbol in the Hörmander class S^b_ρ extends to a bounded operator σ(x,D)\colon M^s,α_p,q(ℝⁿ) → M^s-b,α_p,q(ℝⁿ) provided 0

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