English

Hardy-Steklov operators and embedding inequalities of Sobolev type

Functional Analysis 2017-09-01 v2

Abstract

We characterize a weighted norm inequality which corresponds to the embedding of a class of absolutely continuous functions into the fractional order Sobolev space. The auxiliary result of the paper is of independent interest. It comprises of several types of necessary and sufficient conditions for the boundedness of the Hardy--Steklov operator (an integral operator with two variable boundaries of integration) in weighted Lebesgue spaces.

Keywords

Cite

@article{arxiv.1503.06518,
  title  = {Hardy-Steklov operators and embedding inequalities of Sobolev type},
  author = {Maria G. Nasyrova and Elena P. Ushakova},
  journal= {arXiv preprint arXiv:1503.06518},
  year   = {2017}
}