On a Problem of Jaak Peetre Concerning Pointwise Multipliers of Besov Spaces

TL;DR

This paper characterizes the set of pointwise multipliers for Besov spaces $B^s_{p,q}( )$ when $s > d/p$, providing a comprehensive understanding of how these multipliers behave under certain smoothness and integrability conditions.

Contribution

It offers a complete characterization of pointwise multipliers for Besov spaces $B^s_{p,q}( )$ under specific parameter restrictions, advancing the theoretical understanding of these function spaces.

Findings

Identifies the set of all pointwise multipliers for $B^s_{p,q}( )$ when $s > d/p$.

Provides explicit descriptions of multipliers in terms of Besov space properties.

Enhances the theoretical framework for analyzing function space multipliers.

Abstract

We characterize the set of all pointwise multipliers of the Besov spaces $B^s_{p,q}(\R)$ under the restrictions $0 < p,q \le \infty$ and $s>d/p$.