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

2008/02/07 by Stathis Filippas, Filippas, Stathis, Achilles Tertikas +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Hardy space #Inequality #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Pure mathematics #Sobolev space #Spectral Theory (math.SP) #math.AP #math.SP

paper · pdf · doi:10.48550/arxiv.0802.0986

published in arXiv (Cornell University) (Cornell University) · 20 pages

arxiv created 2008/02/07 · openalex publication_date 2008/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this article 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.

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