Abstract
$L_p-L_q$--boundedness of the map $f\to w(x)\int_{a(x)}^{b(x)}k(x,y)f(y)v(y)dy$ is described by different types of criteria expressed in terms of given parameters $p,q \in (0,\infty)$, strictly increasing boundaries $a(x)$ and $b(x)$, locally integrable weight functions $v,w$ and a positive continuous kernel $k(x,y)$ satisfying some growth conditions.
Citation
V. D. Stepanov. E. P. Ushakova. "On boundedness of a certain class of Hardy--Steklov type operators in Lebesgue spaces." Banach J. Math. Anal. 4 (1) 28 - 52, 2010. https://doi.org/10.15352/bjma/1272374670
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