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

Viktor Kolyada

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

Classical Analysis and ODEs 2018-09-19 v1

Authors: Viktor Kolyada

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 $W_1^1(\mathbb R^n).$

Keywords

sobolev spaces hardy-sobolev spaces besov spaces embedding theorems fourier transforms mixed norms

Cite

@article{arxiv.1809.06602,
  title  = {Embedding theorems for Sobolev and Hardy-Sobolev spaces and estimates of Fourier transforms},
  author = {Viktor Kolyada},
  journal= {arXiv preprint arXiv:1809.06602},
  year   = {2018}
}

Comments

To appear in Ann. Mat. Pura Appl

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