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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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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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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| author | Xiangxing Tao Xiao Yu Songyan Zhang |
| author_facet | Xiangxing Tao Xiao Yu Songyan Zhang |
| author_sort | Xiangxing Tao |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-c12c3cc9add94153a9b531c51086cd14 |
| institution | DOAJ |
| issn | 0972-6802 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-c12c3cc9add94153a9b531c51086cd142025-08-20T03:23:24ZengWileyJournal 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 |
| spellingShingle | Xiangxing Tao Xiao Yu Songyan Zhang Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces Journal of Function Spaces and Applications |
| title | 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_short | Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces |
| title_sort | marcinkiewicz integrals with variable kernels on hardy and weak hardy spaces |
| url | http://dx.doi.org/10.1155/2010/271905 |
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