Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces

Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces

One-weight inequalities with general weights for Riemann-Liouville transform and n-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on Rn are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these op...

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Main Authors: Muhammad Sarwar, Ghulam Murtaza, Irshaad Ahmed
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/621857
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spelling doaj-6a40af81a8da479bb162e716739ced6f2020-11-25T00:21:36ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/621857621857Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) SpacesMuhammad Sarwar0Ghulam Murtaza1Irshaad Ahmed2Department of Mathematics, University of Malakand, Chakdara, Lower Dir 18800, PakistanDepartment of Mathematics, GC University, Faisalabad, Faisalabad 38000, PakistanDepartment of Mathematics, GC University, Faisalabad, Faisalabad 38000, PakistanOne-weight inequalities with general weights for Riemann-Liouville transform and n-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on Rn are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in Lp(x) spaces.http://dx.doi.org/10.1155/2014/621857
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Sarwar
Ghulam Murtaza
Irshaad Ahmed
spellingShingle Muhammad Sarwar
Ghulam Murtaza
Irshaad Ahmed
Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
Abstract and Applied Analysis
author_facet Muhammad Sarwar
Ghulam Murtaza
Irshaad Ahmed
author_sort Muhammad Sarwar
title Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
title_short Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
title_full Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
title_fullStr Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
title_full_unstemmed Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function in Lp(·) Spaces
title_sort riemann-liouville and higher dimensional hardy operators for nonnegative decreasing function in lp(·) spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description One-weight inequalities with general weights for Riemann-Liouville transform and n-dimensional fractional integral operator in variable exponent Lebesgue spaces defined on Rn are investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions in Lp(x) spaces.
url http://dx.doi.org/10.1155/2014/621857
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AT ghulammurtaza riemannliouvilleandhigherdimensionalhardyoperatorsfornonnegativedecreasingfunctioninlpspaces
AT irshaadahmed riemannliouvilleandhigherdimensionalhardyoperatorsfornonnegativedecreasingfunctioninlpspaces
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