Hardy operator with variable limits on monotone functions

We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator...

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Main Authors: Vladimir D. Stepanov, Elena P. Ushakova
Format: Article
Language:English
Published: Wiley 2003-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2003/860547
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author Vladimir D. Stepanov
Elena P. Ushakova
author_facet Vladimir D. Stepanov
Elena P. Ushakova
author_sort Vladimir D. Stepanov
collection DOAJ
description We characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits.
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spelling doaj-art-a821a05cde624bb98f2c709870a86bcb2025-08-20T03:39:09ZengWileyJournal of Function Spaces and Applications0972-68022003-01-011111510.1155/2003/860547Hardy operator with variable limits on monotone functionsVladimir D. Stepanov0Elena P. Ushakova1Department of Mathematics, KAIST, 373-1 Kusong-Dong, Yusong-Gu, Taejon, 305-701, Republic of KoreaComputing Centre FEB RAS, Tikhookeanskaya 153, Khabarovsk, 680042, RussiaWe characterize weighted Lp-Lq inequalities with the Hardy operator of the form Hf(x)=∫a(x)b(x)f(y)u(y) dy with a non-negative weight function u, restricted to the cone of monotone functions on the semiaxis. The proof is based on the Sawyer criterion and the boundedness of generalized Hardy operator with variable limits.http://dx.doi.org/10.1155/2003/860547
spellingShingle Vladimir D. Stepanov
Elena P. Ushakova
Hardy operator with variable limits on monotone functions
Journal of Function Spaces and Applications
title Hardy operator with variable limits on monotone functions
title_full Hardy operator with variable limits on monotone functions
title_fullStr Hardy operator with variable limits on monotone functions
title_full_unstemmed Hardy operator with variable limits on monotone functions
title_short Hardy operator with variable limits on monotone functions
title_sort hardy operator with variable limits on monotone functions
url http://dx.doi.org/10.1155/2003/860547
work_keys_str_mv AT vladimirdstepanov hardyoperatorwithvariablelimitsonmonotonefunctions
AT elenapushakova hardyoperatorwithvariablelimitsonmonotonefunctions