# Pointwise Multipliers for Besov Spaces of Dominating Mixed Smoothness - II

## TL;DR

This paper extends the study of pointwise multipliers for Besov spaces of dominating mixed smoothness, focusing on algebra properties and characterizing multiplier spaces when p ≤ q.

## Contribution

It provides new results on the algebra property of these Besov spaces and characterizes the space of all pointwise multipliers for certain parameter ranges.

## Key findings

- Established algebra property of $S^r_{p,q}B(R^d)$ spaces.
- Characterized pointwise multiplier space when p ≤ q.
- Extended previous investigations on multipliers for Besov spaces.

## Abstract

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes $S^r_{p,q}B(\mathbb{R}^d)$ with respect to pointwise multiplication. In addition if $p\leq q$, we are able to describe the space of all pointwise multipliers for $S^r_{p,q}B(\mathbb{R}^d)$.