Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces
In this article, we consider the Marcinkiewicz integrals with variable kernels defined by μΩ(f)(x)=(∫0∞|∫|x−y|≤tΩ(x,x−y)|x−y|n−1f(y)dy|2dtt3)1/2, where Ω(x,z)∈L∞(ℝn)×Lq(Sn−1) for q > 1. We prove that the operator μΩ is bounded from Hardy space, Hp(ℝn), to Lp(ℝn) space; and is bounded from weak Ha...
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Series: | Journal of Function Spaces and Applications |
Online Access: | http://dx.doi.org/10.1155/2010/271905 |
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doaj-c12c3cc9add94153a9b531c51086cd142020-11-25T01:09:25ZengHindawi LimitedJournal of Function Spaces and Applications0972-68022010-01-018111610.1155/2010/271905Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spacesXiangxing Tao0Xiao Yu1Songyan Zhang2Department of Mathematics, Zhejiang University of Science & Technology, Hangzhou, Zhejiang province, 310023, ChinaDepartment of Mathematics, Zhejiang University of Science & Technology, Hangzhou, Zhejiang province, 310023, ChinaDepartment of Mathematics, Zhejiang University of Science & Technology, Hangzhou, Zhejiang province, 310023, ChinaIn this article, we consider the Marcinkiewicz integrals with variable kernels defined by μΩ(f)(x)=(∫0∞|∫|x−y|≤tΩ(x,x−y)|x−y|n−1f(y)dy|2dtt3)1/2, where Ω(x,z)∈L∞(ℝn)×Lq(Sn−1) for q > 1. We prove that the operator μΩ is bounded from Hardy space, Hp(ℝn), to Lp(ℝn) space; and is bounded from weak Hardy space, Hp,∞(ℝn), to weak Lp(ℝn) space for max{2n2n+1,nn+α}<p<1, if Ω satisfies the L1,α-Dini condition with any 0<α≤1.http://dx.doi.org/10.1155/2010/271905 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Xiangxing Tao Xiao Yu Songyan Zhang |
spellingShingle |
Xiangxing Tao Xiao Yu Songyan Zhang Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces Journal of Function Spaces and Applications |
author_facet |
Xiangxing Tao Xiao Yu Songyan Zhang |
author_sort |
Xiangxing Tao |
title |
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
title_short |
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
title_full |
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
title_fullStr |
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
title_full_unstemmed |
Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
title_sort |
marcinkiewicz integrals with variable kernels on hardy and weak hardy spaces |
publisher |
Hindawi Limited |
series |
Journal of Function Spaces and Applications |
issn |
0972-6802 |
publishDate |
2010-01-01 |
description |
In this article, we consider the Marcinkiewicz integrals with variable kernels defined by μΩ(f)(x)=(∫0∞|∫|x−y|≤tΩ(x,x−y)|x−y|n−1f(y)dy|2dtt3)1/2, where Ω(x,z)∈L∞(ℝn)×Lq(Sn−1) for q > 1. We prove that the operator μΩ is bounded from Hardy space, Hp(ℝn), to Lp(ℝn) space; and is bounded from weak Hardy space, Hp,∞(ℝn), to weak Lp(ℝn) space for max{2n2n+1,nn+α}<p<1, if Ω satisfies the L1,α-Dini condition with any 0<α≤1. |
url |
http://dx.doi.org/10.1155/2010/271905 |
work_keys_str_mv |
AT xiangxingtao marcinkiewiczintegralswithvariablekernelsonhardyandweakhardyspaces AT xiaoyu marcinkiewiczintegralswithvariablekernelsonhardyandweakhardyspaces AT songyanzhang marcinkiewiczintegralswithvariablekernelsonhardyandweakhardyspaces |
_version_ |
1725178969590857728 |