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2013 On the boundedness and compactness of a certain integral operator
S. M. Farsani
Banach J. Math. Anal. 7(2): 86-102 (2013). DOI: 10.15352/bjma/1363784225

Abstract

Let $\alpha \in (0, \infty)$ and $\beta \in (1, \infty)$. In the present work, the necessary and sufficient conditions for the boundedness and compactness of the integral operator of the form \begin{equation*} L_{\alpha, \beta} f(x):=v(x)\int_0^x \frac{\ln^{\beta-1}(\frac{x}{y})f(y)u(y)dy}{(x-y)^{1-\alpha}} ,\,\,\,\, x>0, \end{equation*} from $L^p\to L^q$, with locally integrable non-negative weight functions $u$ and $v$, in the case $p,q \in (0, \infty), p>\max(1/{\alpha},1),$ provided $u$ is non-increasing on $\mathbb{R}^+:=[0,\infty)$ are found.

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S. M. Farsani . "On the boundedness and compactness of a certain integral operator." Banach J. Math. Anal. 7 (2) 86 - 102, 2013. https://doi.org/10.15352/bjma/1363784225

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1270.26019
MathSciNet: MR3039941
Digital Object Identifier: 10.15352/bjma/1363784225

Subjects:
Primary: 26D10
Secondary: 26D07 , 26D15 , 47G10

Keywords: boundedness , compactness , Integral‎ ‎Operators , weights‎

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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