Estimates for entropy numbers of embedding operators of function spaces on sets with tree-like structure: some limiting cases

TL;DR

This paper provides order estimates for the entropy numbers of embedding operators between weighted Sobolev and Lebesgue spaces, as well as for weighted summation operators on trees, under critical parameter conditions.

Contribution

It introduces new order estimates for entropy numbers in the context of weighted function space embeddings and summation operators on trees, especially in critical cases.

Findings

Derived order estimates for entropy numbers of embeddings

Analyzed weighted Sobolev to Lebesgue space embeddings

Studied weighted summation operators on trees

Abstract

In this paper we obtain order estimates for entropy numbers of embeddings of weighted Sobolev spaces into weighted Lebesgue spaces and of weighted summation operators on trees. Here we consider some critical conditions on the parameters.