Stypyalis, Lyudvikas On a variant of the Hardy-Littlewood inequality. (Russian. English summary) Zbl 0566.26004 Differ. Uravn. Primen. 34, 129-134 (1983). Let \(1\leq m\leq n\), \(x=(x_ 1,...,x_ n)\in R^ n\), \(x'=(x_ 1,...,x_ m)\), \(1\leq p\leq \infty,\) \(p^{-1}+q^{-1}=1,\) \(\lambda <m/p,\) \(\mu <n/q,\) \(\lambda +\mu >0.\) Let \(| \cdot |\) denote the Euclidean norm. Let \(K(x,t)=| x'|^{-\lambda}| x- t|^{\lambda +\mu -n}| t'|^{-\mu}\) and \[ (Tf)(x)=\int_{R^ n}K(x,t)f(t)dt \] for f in \(L_ p(R^ n).\) The author proves that the operator T is bounded on \(L_ p(R^ n).\) Reviewer: I.Raşa MSC: 26D10 Inequalities involving derivatives and differential and integral operators Keywords:Hardy-Littlewood inequality; integral operator PDFBibTeX XMLCite \textit{L. Stypyalis}, Differ. Uravn. Primen. 34, 129--134 (1983; Zbl 0566.26004)