Pointwise Multipliers for Sobolev and Besov Spaces of Dominating Mixed Smoothness
Van Kien Nguyen, Winfried Sickel
TL;DR
This paper characterizes pointwise multipliers for Sobolev and Besov spaces with dominating mixed smoothness, providing conditions for these spaces to be algebras under pointwise multiplication.
Contribution
It offers a comprehensive description of pointwise multipliers and algebra conditions for these specialized function spaces, extending existing theory.
Findings
Characterization of all pointwise multipliers under certain restrictions
Necessary and sufficient conditions for these spaces to be algebras
Extension of multiplier theory to spaces of dominating mixed smoothness
Abstract
Under certain restrictions we describe the set of all pointwise multipliers in case of Sobolev and Besov spaces of dominating mixed smoothness. In addition we shall give necessary and sufficient conditions for the case that these spaces form algebras with respect to pointwise multiplication.
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