Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms

TL;DR

This paper establishes improved embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces with mixed norms and derives Fourier transform estimates for functions in Sobolev spaces, enhancing existing theoretical frameworks.

Contribution

It introduces new embeddings into Besov spaces with mixed norms and applies these to obtain Fourier transform estimates for Sobolev space functions, improving prior results.

Findings

Enhanced embeddings of Sobolev spaces into Besov spaces with mixed norms

Improved Fourier transform estimates for Sobolev space functions

Extension of Oberlin type estimates to broader function classes

Abstract

We prove embeddings of Sobolev and Hardy-Sobolev spaces into Besov spaces built upon certain mixed norms. This gives an improvment of the known embeddings into usual Besov spaces. Applying these results, we obtain Oberlin type estimates of Fourier transforms for functions in Sobolev spaces $W_1^1(\mathbb R^n).$