Difference Norms for Vector-Valued Bessel Potential Spaces with an Application to Pointwise Multipliers
| Autor: | Nick Lindemulder |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Pointwise Pure mathematics Mathematics::Functional Analysis 46E40 (Primary) 42B15 46B09 46B09 46E30 46E35 (Secondary) 010102 general mathematics Banach space Mathematics::Classical Analysis and ODEs Bessel potential 01 natural sciences Functional Analysis (math.FA) 010101 applied mathematics Multiplier (Fourier analysis) Mathematics - Functional Analysis Indicator function Norm (mathematics) FOS: Mathematics Interpolation space 0101 mathematics Lp space Analysis Mathematics |
| Popis: | In this paper we prove a randomized difference norm characterization for Bessel potential spaces with values in UMD Banach spaces. The main ingredients are $\mathcal{R}$-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. 32 pages, accepted for publication in Journal of Functional Analysis |
| Databáze: | OpenAIRE |
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