Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces
作者: Bo LiMinfeng LiaoBaode Li
作者单位: 1Xinjiang University
刊名: Journal of Inequalities and Applications, 2017, Vol.2017 (1)
来源数据库: Springer Journal
DOI: 10.1186/s13660-017-1501-1
关键词: Marcinkiewicz integralMuckenhoupt weightMusielak-Orlicz functionHardy space42B2042B3046E30
英文摘要: Let \(\varphi:\mathbb{R}^{n}\times[0, \infty) \to[0, \infty)\) satisfy that \(\varphi(x, \cdot)\) , for any given \(x\in\mathbb{R}^{n}\) , is an Orlicz function and \(\varphi(\cdot, t)\) is a Muckenhoupt \(A_{\infty}\) weight uniformly in \(t\in(0, \infty)\) . The Musielak-Orlicz Hardy space \(H^{\varphi}(\mathbb{R}^{n})\) is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz space \(L^{\varphi}(\mathbb{R}^{n})\) . In this paper, the authors establish the boundedness of Marcinkiewicz integral \(\mu _{\Omega}\) from \(H^{\varphi}(\mathbb{R}^{n})\) to \(L^{\varphi}(\mathbb{R}^{n})\) under weaker smoothness conditions assumed on Ω. This result is also new even when \(\varphi(x, t):=\phi(t)\) for all \((x,...
原始语种摘要: Let \(\varphi:\mathbb{R}^{n}\times[0, \infty) \to[0, \infty)\) satisfy that \(\varphi(x, \cdot)\) , for any given \(x\in\mathbb{R}^{n}\) , is an Orlicz function and \(\varphi(\cdot, t)\) is a Muckenhoupt \(A_{\infty}\) weight uniformly in \(t\in(0, \infty)\) . The Musielak-Orlicz Hardy space \(H^{\varphi}(\mathbb{R}^{n})\) is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz space \(L^{\varphi}(\mathbb{R}^{n})\) . In this paper, the authors establish the boundedness of Marcinkiewicz integral \(\mu _{\Omega}\) from \(H^{\varphi}(\mathbb{R}^{n})\) to \(L^{\varphi}(\mathbb{R}^{n})\) under weaker smoothness conditions assumed on Ω. This result is also new even when \(\varphi(x, t):=\phi(t)\) for all \((x,...
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影响因子:0.822 (2012)

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关键词翻译
关键词翻译
  • integral 积分
  • boundedness 有界性
  • maximal 最大的
  • grand 宏伟的
  • smoothness 平滑度
  • defined 定义
  • weight 
  • tempered 回火
  • Omega 希腊字母的最后一字(Ω,ω)奥米伽(导航系统)希腊字母的末一字
  • assumed 假定的