# Entropy numbers of compact embeddings of Smoothness Morrey spaces on bounded domains

## TL;DR

This paper investigates the entropy numbers of compact embeddings between smoothness Morrey spaces on bounded domains, revealing a new phenomenon related to the smoothness parameters and employing wavelet techniques for analysis.

## Contribution

It characterizes the entropy numbers of these embeddings and uncovers a novel behavior when the smoothness difference is small, using wavelet decomposition methods.

## Key findings

- Discovered a new phenomenon in entropy numbers related to smoothness parameters.
- Provided a detailed characterization of the entropy numbers for these embeddings.
- Utilized wavelet techniques to analyze the sequence space setting.

## Abstract

We study the compact embedding between smoothness Morrey spaces on bounded domains and characterise its entropy numbers. Here we discover a new phenomenon when the difference of smoothness parameters in the source and target spaces is rather small compared with the influence of the fine parameters in the Morrey setting. In view of some partial forerunners this was not to be expected till now. Our argument relies on wavelet decomposition techniques of the function spaces and a careful study of the related sequence space setting.