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

Nick Lindemulder

doi:10.1016/j.jfa.2016.11.009

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

Nick Lindemulder

Analysis

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3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1435-1476
Number of pages	42
Journal	Journal of Functional Analysis
Volume	272
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2016.11.009
Publication status	Published - 2017

Keywords

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

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10.1016/j.jfa.2016.11.009

Cite this

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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.",

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KW - R-boundedness of Fourier multipliers

KW - UMD space-valued Bessel potential space

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

Abstract

Keywords

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