Potential operators on cones of nonincreasing functions
type: Item
instance of: scholarly article
title: Potential operators on cones of nonincreasing functions
zbMATH Open document ID: 1237.47054
DOI: 10.1155/2012/474681
author: Alexander Meskhi
author: Ghulam Murtaza
published in: Journal of Function Spaces and Applications
publication date: 2012-05-10T00:00:00Z
review text: Summary: Necessary and sufficient conditions on weight pairs guaranteeing the two-weight inequalities for the potential operators \((I_\alpha f)(x) = \int^\infty_0(f(t)/|x - t|^{1-\alpha})\,dt\) and \((\mathcal I_{\alpha_1,\alpha_2} f)(x, y) = \int^\infty_0 \int^\infty_0 (f(t, \tau)/|x - t|^{1-\alpha_1}|y - \tau|^{1-\alpha_2})\,dt\,d\tau\) on the cone of nonincreasing functions are derived. In the case of \(\mathcal I_{\alpha_1,\alpha_2}\), we assume that the right-hand side weight is of product type. The same problem for other mixed-type double potential operators is also studied. Exponents of the Lebesgue spaces are assumed to be between \(1\) and \(\infty\).
Mathematics Subject Classification ID: 47G40
zbMATH DE Number: 6032363
Wikidata QID: Q58908280
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/474681
OpenAlex ID: W2052539491
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description: scientific article; zbMATH DE number 6032363