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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer Berlin Heidelberg

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DOI

10.1002/zaac.19050460106

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1432-1807

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Weighted Calderón–Zygmund and Rellich inequalities

Authors: Giorgio Metafune Motohiro Sobajima Chiara Spina
Publish Date: 2014/07/20
Volume: 361, Issue: 1-2, Pages: 313-366
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Abstract

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderón–Zygmund inequalities with respect to Lpnorm 1le p le infty for functions in the whole space and in the halfspace with Dirichlet boundary conditions General operators like L=varDelta +cfracxx2cdot nabla fracbx2 are considered We compute best constants in some situationsIn this appendix we state and proof three inequalities of Hardy type we need in the paper The first two are wellknown in the literature but we give a short proof for completeness Proposition 83 ii seems to be new concerning the computation of the best constantThe proof is identical to that given in 13 Theorem 34 In fact for every fin C bvarOmega a solution u of 59 can be obtained as limit of solutions u n of the Dirichlet problems associated with the operator above in the sequence of annuli B nsetminus B frac1n which fill the whole varOmega square

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