Weighted Calderón-Zygmund and Rellich inequalities in \(L^p\)

DOI10.1007/s00208-014-1075-xzbMath1318.26038arXiv1309.1302OpenAlexW2020418212MaRDI QIDQ2255281

Motohiro Sobajima, Chiara Spina, Metafune, Giorgio

Publication date: 9 February 2015

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.1302

zbMATH Keywords

Hardy-type inequalitiesRellich inequalitybest constantsweighted Calderón-Zygmund estimates

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Maximum principles in context of PDEs (35B50) Degenerate elliptic equations (35J70) General theory of partial differential operators (47F05) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (26)

A sequence of weighted Birman-Hardy-Rellich inequalities with logarithmic refinements ⋮ Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs ⋮ A general approach to weighted \(L^{p}\) Rellich type inequalities related to Greiner operator ⋮ Kernel estimates for Schrödinger type operators with unbounded coefficients and critical exponents ⋮ Improved higher order Poincaré inequalities on the hyperbolic space via Hardy-type remainder terms ⋮ Optimality of constants in power-weighted Birman-Hardy-Rellich-Type inequalities with logarithmic refinements ⋮ Kernel estimates for elliptic operators with second-order discontinuous coefficients ⋮ Local existence and uniqueness of Euler equation in weighted Sobolev space ⋮ Uniform resolvent and Strichartz estimates for Schrödinger equations with critical singularities ⋮ \(L^p\) estimates for the Caffarelli-Silvestre extension operators ⋮ On global existence for semilinear wave equations with space-dependent critical damping ⋮ On some strong Poincaré inequalities on Riemannian models and their improvements ⋮ Eigenvalue bounds for non-self-adjoint Schrödinger operators with the inverse-square potential ⋮ Weighted Rellich type inequalities related to Baouendi-Grushin operators ⋮ A unified approach to degenerate problems in the half-space ⋮ Anisotropic Sobolev spaces with weights ⋮ Fourth‐order Schrödinger type operator with unbounded coefficients in L²(ℝ^N) ⋮ Characterizations of weighted Hardy-Rellich inequalities and their applications ⋮ Rellich inequalities in bounded domains ⋮ Sharp Poincaré-Hardy and Poincaré-Rellich inequalities on the hyperbolic space ⋮ A general approach to weighted Rellich type inequalities on Carnot groups ⋮ Remarks on endpoint Strichartz estimates for Schrödinger equations with the critical inverse-square potential ⋮ \(L^p\) estimates for Baouendi-Grushin operators ⋮ HARDY AND RELLICH INEQUALITIES ON THE COMPLEMENT OF CONVEX SETS ⋮ Rellich and Calderón-Zygmund inequalities for an operator with discontinuous coefficients ⋮ On higher order Poincaré inequalities with radial derivatives and Hardy improvements on the hyperbolic space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rellich inequalities with weights
• Weighted Sobolev spaces of radially symmetric functions
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• \(L^{p}\)-theory for some elliptic and parabolic problems with first order degeneracy at the boundary
• Gaussian estimates and interpolation of the spectrum in \(L^ p\)
• Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
• A simple approach to Hardy inequalities
• Optimal Rellich-Sobolev constants and their extremals.
• An integration by parts formula in Sobolev spaces
• Elliptic operators with unbounded diffusion and drift coefficients in \(L^p\)
• Generation results for elliptic operators with unbounded diffusion coefficients in \(L^p\)-and \(C_b\)-spaces
• A degenerate elliptic operator with unbounded diffusion coefficients
• Sur les multiplicateurs dans \({\mathcal F}L^ p\) avec poids
• Elliptic operators with unbounded diffusion coefficients in $L^p$ spaces
• Note on Singular Integrals
• Schrödinger operators with l l/2w(Rl) -potentials
• One-Parameter Semigroups for Linear Evolution Equations
• SPECTRAL PROPERTIES OF THE OPERATOR EQUATION AX + XB = Y
• Compactness properties of Feller semigroups
• Weighted Norm Inequalities for Singular and Fractional Integrals

This page was built for publication: Weighted Calderón-Zygmund and Rellich inequalities in \(L^p\)