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

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

Journal Article (2017)

Author(s)

Nick Lindemulder (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Research Group

Analysis

Pointwise multiplier Difference norm R-boundedness of Fourier multipliers UMD space-valued Bessel potential space

DOI related publication

https://doi.org/10.1016/j.jfa.2016.11.009 Final published version

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https://resolver.tudelft.nl/uuid:cea52efa-fd2c-4c52-97a7-46a91e785e58

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Publication Year

2017

Language

English

Research Group

Analysis

Journal title

Journal of Functional Analysis

Issue number

4

Volume number

272

Pages (from-to)

1435-1476

Downloads counter

152

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.