Dilation in function spaces with general weights

TL;DR

This paper investigates conditions under which dilation operators are bounded on weighted Besov and Triebel-Lizorkin spaces, enhancing understanding of their regularity properties.

Contribution

It introduces new regularity conditions that guarantee the boundedness of dilation operators on these weighted function spaces.

Findings

Established new regularity conditions for dilation boundedness.

Extended previous results to more general weights.

Provided theoretical framework for further analysis of weighted spaces.

Abstract

In this paper, we present more regularity conditions which ensure the boundedness of dilation operators on Besov and Triebel-Lizorkin spaces equiped with general weights.