Hardy type operators on grand Lebesgue spaces for non-increasing functions

Hardy type operators on grand Lebesgue spaces for non-increasing functions

We characterize the weights w for which the operator Tψf(x)=∫0xψ(x,y)f(y)dy is bounded between weighted grand Lebesgue spaces Lwp) for non-increasing functions. The conjugate of Tψ, for a special ψ, given by Sϕ∗f(x):=∫x∞f(y)ϕ(y)Φ(y)dy is considered. An extrapolation type result giving Lp)-boundednes...

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Main Authors: Pankaj Jain, Monika Singh, Arun Pal Singh
Format: Article
Language:English
Published: Elsevier 2016-05-01
Series:Transactions of A. Razmadze Mathematical Institute
Online Access:http://www.sciencedirect.com/science/article/pii/S2346809216000143
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spelling doaj-4d2e14e8c9e84a5a8e4077395aa70d512020-11-24T22:49:52ZengElsevierTransactions of A. Razmadze Mathematical Institute2346-80922016-05-0117013446Hardy type operators on grand Lebesgue spaces for non-increasing functionsPankaj Jain0Monika Singh1Arun Pal Singh2Department of Mathematics, Faculty of Mathematics and Computer Science, South Asian University, Akbar Bhawan, Chanakya Puri, New Delhi–110 021, India; Corresponding author.Department of Mathematics, Lady Shri Ram College For Women (University of Delhi), Lajpat Nagar, New Delhi–110 024, IndiaDepartment of Mathematics, Dyal Singh College (University of Delhi), Lodhi Road, New Delhi–110 003, IndiaWe characterize the weights w for which the operator Tψf(x)=∫0xψ(x,y)f(y)dy is bounded between weighted grand Lebesgue spaces Lwp) for non-increasing functions. The conjugate of Tψ, for a special ψ, given by Sϕ∗f(x):=∫x∞f(y)ϕ(y)Φ(y)dy is considered. An extrapolation type result giving Lp)-boundedness of Sϕ∗ for non-increasing functions has been proved. Also its Lp-boundedness has been characterized. Finally, a variant of Sϕ∗ has been considered and discussed. Keywords: Non-increasing functions, Bϕ,p class of weights, Bϕ,p∗ class of weights, grand Lebesgue spacehttp://www.sciencedirect.com/science/article/pii/S2346809216000143
collection DOAJ
language English
format Article
sources DOAJ
author Pankaj Jain
Monika Singh
Arun Pal Singh
spellingShingle Pankaj Jain
Monika Singh
Arun Pal Singh
Hardy type operators on grand Lebesgue spaces for non-increasing functions
Transactions of A. Razmadze Mathematical Institute
author_facet Pankaj Jain
Monika Singh
Arun Pal Singh
author_sort Pankaj Jain
title Hardy type operators on grand Lebesgue spaces for non-increasing functions
title_short Hardy type operators on grand Lebesgue spaces for non-increasing functions
title_full Hardy type operators on grand Lebesgue spaces for non-increasing functions
title_fullStr Hardy type operators on grand Lebesgue spaces for non-increasing functions
title_full_unstemmed Hardy type operators on grand Lebesgue spaces for non-increasing functions
title_sort hardy type operators on grand lebesgue spaces for non-increasing functions
publisher Elsevier
series Transactions of A. Razmadze Mathematical Institute
issn 2346-8092
publishDate 2016-05-01
description We characterize the weights w for which the operator Tψf(x)=∫0xψ(x,y)f(y)dy is bounded between weighted grand Lebesgue spaces Lwp) for non-increasing functions. The conjugate of Tψ, for a special ψ, given by Sϕ∗f(x):=∫x∞f(y)ϕ(y)Φ(y)dy is considered. An extrapolation type result giving Lp)-boundedness of Sϕ∗ for non-increasing functions has been proved. Also its Lp-boundedness has been characterized. Finally, a variant of Sϕ∗ has been considered and discussed. Keywords: Non-increasing functions, Bϕ,p class of weights, Bϕ,p∗ class of weights, grand Lebesgue space
url http://www.sciencedirect.com/science/article/pii/S2346809216000143
work_keys_str_mv AT pankajjain hardytypeoperatorsongrandlebesguespacesfornonincreasingfunctions
AT monikasingh hardytypeoperatorsongrandlebesguespacesfornonincreasingfunctions
AT arunpalsingh hardytypeoperatorsongrandlebesguespacesfornonincreasingfunctions
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