Weighted Calderon-Zygmund and Rellich inequalities in L^p

2013/09/05 by Giorgio Metafune, Metafune, G., Motohiro Sobajima +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1309.1302

openalex publication_date 2013/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderon-Zygmund inequalities in L^p, 1 ≤ p ≤ ∞, in the whole space and in the half-space with Dirichlet boundary conditions. General operators like L=Δ+c(x)/(|x|²)⋅∇-(b)/(|x|²) are considered. We compute best constants in some situations.

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• Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem

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