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

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• 作者：Nick Lindemulder ^{N.Lindemulder@tudelft.nl}
• 关键词：primary ; 46E40 ; secondary ; 42B15 ; 46B09 ; 46E30 ; 46E35
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：272
• 期：4
• 页码：1435-1476
• 全文大小：766 K
• 卷排序：272

文摘

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.