Difference Norms for Vector-Valued Bessel Potential Spaces with an Application to Pointwise Multipliers

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 $\mathcal{R}$-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

References in corpus (4)

• Stochastic maximal $L^p$-regularity
• The $H^{\infty }$-Functional Calculus and Square Function Estimates
• On the ${\ell }^s$-boundedness of a family of integral operators
• On the R-boundedness of stochastic convolution operators

Cited by in corpus (1)

• An Intersection Representation for a Class of Anisotropic Vector-valued Function Spaces