Lusin functions and nontangential maximal functions in the \(H^ p\) theory on the product of upper half-spaces
Let us consider a biharmonic function u, defined on the product space \(D={\mathbb{R}}_+^{n+1}\times {\mathbb{R}}_+^{m+1},\) where \({\mathbb{R}}_+^{n+1}={\mathbb{R}}^ n\times (0,\infty).\) Let A(u) be the Lusin area integral of the biharmonic function u and N(u) its nontangential maximal function. In this paper the author proves the following inequalities: \(\| A(u)\|_ p\leq c_ p \| N(u)\|_ p\) and \(\| N(u)\|_ p\leq c_ p \| A(u)\|_ p,\) where \(c_ p\) is a constant independent of u, \(\| \cdot \|_ p\) is a norm in \(H^ p(D)\) space.
scientific article; zbMATH DE number 3904945