More on hypersingular integrals and embeddings into hölder spaces

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro, Stefan Samko

Research output: Chapter in Book/Report/Conference proceedingChapter

2 Citations (Scopus)


In this chapter we present results on hypersingular operators of order α < 1 acting on some Sobolev type variable exponent spaces, where the underlying space is a quasimetric measure space. The proofs are based on some pointwise estimations of differences of Sobolev functions. These estimates lead also to embeddings of variable exponent Hajlasz-Sobolev spaces into variable order Hölder spaces. In the Euclidean case we prove denseness of C0-functions in W1,p(·)(Rn). Note that in this chapter we consider quasimetric measure spaces with symmetric distance: d(x, y) = d(y, x).

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Number of pages16
Publication statusPublished - Jan 1 2016
Externally publishedYes

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

ASJC Scopus subject areas

  • Analysis


Dive into the research topics of 'More on hypersingular integrals and embeddings into hölder spaces'. Together they form a unique fingerprint.

Cite this