## Banach Journal of Mathematical Analysis

### 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.

#### Article information

Source
Banach J. Math. Anal., Volume 4, Number 1 (2010), 28-52.

Dates
First available in Project Euclid: 27 April 2010

https://projecteuclid.org/euclid.bjma/1272374670

Digital Object Identifier
doi:10.15352/bjma/1272374670

Mathematical Reviews number (MathSciNet)
MR2593905

Zentralblatt MATH identifier
1193.26013

#### Citation

Stepanov, V. D.; Ushakova, E. P. On boundedness of a certain class of Hardy--Steklov type operators in Lebesgue spaces. Banach J. Math. Anal. 4 (2010), no. 1, 28--52. doi:10.15352/bjma/1272374670. https://projecteuclid.org/euclid.bjma/1272374670

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