The $\infty$-Besov Capacity Problem

TL;DR

This paper develops a comprehensive theory of $ abla$-Besov capacities, solving an open problem, deriving new inequalities, and characterizing multipliers in $ abla$-Besov spaces, advancing the understanding of these function spaces.

Contribution

It introduces a new theory of $ abla$-Besov capacities, addressing an open problem and providing new inequalities and multiplier characterizations.

Findings

Solved an open problem in $ abla$-Besov semi-norm limits

Derived new restriction-extension inequalities

Characterized point-wise multipliers on $ abla$-Besov spaces

Abstract

A theory of $\infty$-Besov capacities is developed and several applications are provided. In particular, we solve an open problem in the theory of limits of the $\infty$-Besov semi-norms, we obtain new restriction-extension inequalities and we characterize the point-wise multipliers acting on the $\infty$-Besov spaces.