Images of integration operators in weighted function spaces

TL;DR

This paper studies the properties of integration operators in weighted Besov and Triebel-Lizorkin spaces, linking their entropy and approximation numbers to embedding operator characteristics.

Contribution

It introduces new connections between integration operators and weighted function space embeddings, focusing on entropy and approximation numbers.

Findings

Established bounds for entropy numbers of integration operators

Linked approximation numbers to embedding characteristics

Analyzed operators in weighted Besov and Triebel-Lizorkin spaces

Abstract

Images of integration operators of natural orders are considered as elements of Besov and Triebel--Lizorkin spaces with local Muckenhoupt weights on $\mathbb{R}^N$. The results connect entropy and approximation numbers of embedding operators with the same characteristics of the integration operators.