On the L² boundedness of pseudo-multipliers for Hermite expansions

2022/03/17 by Ly, Fu Ken
#33C45 #35S05 #42B20 #42C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2203.09058

Abstract

We give various conditions for Hermite pseudo-multipliers to be bounded on L²(ℝⁿ). As a by-product we also give results on L^p(ℝⁿ), as well as new results for pseudo-multipliers for the Gaussian measure setting. One of our key tools is a new integration by-parts formula for Hermite expansions.

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