Two-weighted Hardy operators in $L^{p(\cdot )}$ spaces and applications
Volume 249 / 2019
Studia Mathematica 249 (2019), 143-162
MSC: Primary 46B50; Secondary 46E30.
DOI: 10.4064/sm180204-20-8
Published online: 3 June 2019
Abstract
We establish bounds for the norm of the two-weighted Hardy operator $H_{v,w}$ in variable exponent Lebesgue spaces $L^{p(\cdot )}$. The results derived are applied to (a) estimate the measure of non-compactness for $H_{v,w}$; (b) prove a two-weighted variant of the Rellich inequality in $L^{p(\cdot )}$.
