Fractional Hardy-Sobolev-Maz'ya inequality for domains

Bartłomiej Dyda; Rupert L. Frank

Fractional Hardy-Sobolev-Maz'ya inequality for domains

Functional Analysis 2011-09-30 v1

Authors: Bartłomiej Dyda , Rupert L. Frank

Abstract

We prove a fractional version of the Hardy--Sobolev--Maz'ya inequality for arbitrary domains and $L^p$ norms with $p\geq 2$ . This inequality combines the fractional Sobolev and the fractional Hardy inequality into a single inequality, while keeping the sharp constant in the Hardy inequality.

Keywords

fractional Hardy-Sobolev-Maz'ya inequality arbitrary domains L^p norms fractional Sobolev inequality fractional Hardy inequality sharp constant

Cite

@article{arxiv.1109.6570,
  title  = {Fractional Hardy-Sobolev-Maz'ya inequality for domains},
  author = {Bartłomiej Dyda and Rupert L. Frank},
  journal= {arXiv preprint arXiv:1109.6570},
  year   = {2011}
}

Comments

14 pages

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