A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn

We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators...

Full description

Saved in:
Bibliographic Details
Main Authors: Zun Wei Fu, Shan Zhen Lu, Wen Yuan
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/780132
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849306994056364032
author Zun Wei Fu
Shan Zhen Lu
Wen Yuan
author_facet Zun Wei Fu
Shan Zhen Lu
Wen Yuan
author_sort Zun Wei Fu
collection DOAJ
description We introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in λ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.
format Article
id doaj-art-24ed2eecf0834ba593114d4febd5a9c9
institution Kabale University
issn 1085-3375
1687-0409
language English
publishDate 2012-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-24ed2eecf0834ba593114d4febd5a9c92025-08-20T03:54:53ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/780132780132A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝnZun Wei Fu0Shan Zhen Lu1Wen Yuan2Department of Mathematics, Linyi University, Shandong, Linyi 276005, ChinaSchool of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaSchool of Mathematical Sciences, Beijing Normal University and Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, ChinaWe introduce certain type of weighted variant of Riemann-Liouville fractional integral on ℝn and obtain its sharp bounds on the central Morrey and λ-central BMO spaces. Moreover, we establish a sufficient and necessary condition of the weight functions so that commutators of weighted Hardy operators (with symbols in λ-central BMO space) are bounded on the central Morrey spaces. These results are further used to prove sharp estimates of some inequalities due to Weyl and Cesàro.http://dx.doi.org/10.1155/2012/780132
spellingShingle Zun Wei Fu
Shan Zhen Lu
Wen Yuan
A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
Abstract and Applied Analysis
title A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
title_full A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
title_fullStr A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
title_full_unstemmed A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
title_short A Weighted Variant of Riemann-Liouville Fractional Integrals on ℝn
title_sort weighted variant of riemann liouville fractional integrals on rn
url http://dx.doi.org/10.1155/2012/780132
work_keys_str_mv AT zunweifu aweightedvariantofriemannliouvillefractionalintegralsonrn
AT shanzhenlu aweightedvariantofriemannliouvillefractionalintegralsonrn
AT wenyuan aweightedvariantofriemannliouvillefractionalintegralsonrn
AT zunweifu weightedvariantofriemannliouvillefractionalintegralsonrn
AT shanzhenlu weightedvariantofriemannliouvillefractionalintegralsonrn
AT wenyuan weightedvariantofriemannliouvillefractionalintegralsonrn