Fractional Hardy–Sobolev–Maz'ya inequality for domains

Volume 208 / 2012

Bartłomiej Dyda, Rupert L. Frank Studia Mathematica 208 (2012), 151-166 MSC: Primary 26D10; Secondary 46E35, 31C25. DOI: 10.4064/sm208-2-3


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.


  • Bartłomiej DydaFaculty of Mathematics
    University of Bielefeld
    Postfach 10 01 31
    D-33501 Bielefeld, Germany
    Institute of Mathematics and Computer Science
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
  • Rupert L. FrankDepartment of Mathematics
    Princeton University
    Princeton, NJ 08544, U.S.A.

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