A+ CATEGORY SCIENTIFIC UNIT

Fractional Hardy inequalities and visibility of the boundary

Volume 224 / 2014

Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas Studia Mathematica 224 (2014), 47-80 MSC: Primary 46E35; Secondary 26D15. DOI: 10.4064/sm224-1-3

Abstract

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.

Authors

  • Lizaveta IhnatsyevaDepartment of Mathematics and
    Systems Analysis
    Aalto University
    P.O. Box 11100
    FI-00076 Aalto, Finland
    and
    Department of Mathematics and Statistics
    University of Jyväskylä
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail
  • Juha LehrbäckDepartment of Mathematics and Statistics
    University of Jyväskylä
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail
  • Heli TuominenDepartment of Mathematics and Statistics
    University of Jyväskylä
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail
  • Antti V. VähäkangasDepartment of Mathematics and Statistics
    University of Helsinki
    P.O. Box 68
    FI-00014 University of Helsinki, Finland
    and
    Department of Mathematics and Statistics
    University of Jyväskylä
    P.O. Box 35 (MaD)
    FI-40014 University of Jyväskylä, Finland
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image