Boundedness of Pseudodifferential Operators on Banach Function Spaces

2013/09/02 by Alexei Yu. Karlovich, Karlovich, Alexei Yu.
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1309.0328

Abstract

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space X(ℝⁿ) and on its associate space X'(ℝⁿ), then a pseudodifferential operator Op(a) is bounded on X(ℝⁿ) whenever the symbol a belongs to the Hörmander class S_ρ,δ^n(ρ-1) with 00. This result is applied to the case of variable Lebesgue spaces L^p(⋅)(ℝⁿ).

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