Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces
 作者： Bo Li,  Minfeng Liao,  Baode 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 integral;  Muckenhoupt weight;  Musielak-Orlicz function;  Hardy space;  42B20;  42B30;  46E30; 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 $$(x,... t)\in\mathbb{R}^{n}\times[0, \infty)$$ , where ϕ is an Orlicz function. 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 $$(x,... t)\in\mathbb{R}^{n}\times[0, \infty)$$ , where ϕ is an Orlicz function.

• 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