JournalsjemsVol. 11 , No. 6DOI 10.4171/jems/178

On the structure of Hardy–Sobolev–Maz'ya inequalities

  • Stathis Filippas

    University of Crete, Heraklion, Greece
  • Achilles Tertikas

    University of Crete, Heraklion, Greece
  • Jesper Tidblom

    Erwin Schrödinger Institute (ESI), Wien, Austria
On the structure of Hardy–Sobolev–Maz'ya inequalities cover

Abstract

We establish new improvements of the optimal Hardy inequality in the half-space. We first add all possible linear combinations of Hardy type terms, thus revealing the structure of this type of inequalities and obtaining best constants. We then add the critical Sobolev term and obtain necessary and sufficient conditions for the validity of Hardy–Sobolev–Maz’ya type inequalities.