Morrey--Sobolev inequalities with power weights on the half-space

TL;DR

This paper establishes optimal Morrey--Sobolev inequalities with power weights on the half-space and hyperbolic space, advancing understanding of weighted Sobolev space embeddings in geometric analysis.

Contribution

It proves new Morrey--Sobolev inequalities with power weights on the half-space and hyperbolic space, with optimal estimates up to a constant.

Findings

Optimal Morrey--Sobolev inequalities with power weights established

Results apply to functions on half-space and hyperbolic space

All estimates are sharp up to a multiplicative constant

Abstract

Morrey--Sobolev inequalities are established for functions in weighted Sobolev spaces on the $n$-dimensional half-space, where the weight is a power of the distance to the boundary, as well as for Sobolev spaces on the $n$-dimensional hyperbolic space. All the estimates are optimal up to a multiplicative constant.