A geometric approach to the Calderón-Zygmund estimates
This paper deals with a new proof of the classical Calderón-Zygmund estimates. Let \(B_r=\) \(\{x\in\mathbb{R}^n\mid|x|< r\}\) and \(u\) is a solution of \(\Delta u= f\) in \(B_2\). Then \[ \int_{B_1}|D^2 u|^2 dx\leq C\Biggl(\int_{B_2}|f|^p dx+ \int_{B_2}|u|^p dx\Biggr) \] for any \(1< p<+\infty\). In the proof the author uses among standard arguments the Vitali covering lemma and Hardy-Littlewood maximal function.
scientific article; zbMATH DE number 1941610