Difference norms for vector-valued Bessel potential spaces with an application to pointwise multipliers

Journal article (2017)

Authors

N. Lindemulder Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Pointwise multiplier Difference norm R-boundedness of Fourier multipliers UMD space-valued Bessel potential space
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Published Date

2017

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are RR-boundedness results for Fourier multiplier operators, which are of independent interest. As an application we characterize the pointwise multiplier property of the indicator function of the half-space on these spaces. All results are proved in the setting of weighted spaces.