On boundedness of a certain class of Hardy--Steklov type operators in Lebesgue spaces

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.