Rellich and Calderón-Zygmund inequalities for an operator with discontinuous coefficients
The authors provide necessary and sufficient conditions for the validity of the Rellich and the Calderón-Zygmund inequalities in \(L^p(\mathbb{R}^N)\) for the operator \[ L=\Delta +(a-1)\sum_{i,j=1}^N \dfrac{x_ix_j}{|x|^2}D_{ij}+c\dfrac{x}{|x|^2}\cdot\nabla - \dfrac{b}{|x|^2} \] with \(a>0\) and \(b,c\in\mathbb{R}.\) The approach is that of the authors' paper [Math. Ann. 361, No. 1--2, 313--366 (2015; Zbl 1318.26038)] applied to the operator \[ \tilde L= |x|^\alpha\Delta +\tilde c |x|^{\alpha-1}\dfrac{x}{|x|}\cdot \nabla -\tilde b |x|^{\alpha-2} \] with suitable \(\alpha,\) \(\tilde{c}\) and \(\tilde{c}.\)
scientific article; zbMATH DE number 6614277
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