Boundedness of sublinear operators on product Hardy spaces and its application
Boundedness of sublinear operators on product Hardy spaces and its application
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积Hardy空间上次线性算子的有界性及其应用
DOI：
10.2969/jmsj/06210321
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发表时间：
2009-03
影响因子：
0.7
通讯作者：
Chang, Der-Chen
中科院分区：
文献类型：
--
作者：
Zhou, Yuan;Yang, Dachun;Chang, Der-Chen
Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb R}^n\times{\mathbb R}^m})$ to some quasi-Banach space ${\mathcal B}$ if and only if $T$ maps all $(p, 2, s_1, s_2)$-atoms into uniformly bounded elements of ${\mathcal B}$. Here $s_1\ge\lfloor n(1/p-1)\rfloor$ and $s_2\ge\lfloor m(1/p-1)\rfloor$. As usual, $\lfloor n(1/p-1)\rfloor$ denotes the maximal integer no more than $n(1/p-1)$. Applying this result, the authors establish the boundedness of the commutators generated by Calder\'on-Zygmund operators and Lipschitz functions from the Lebesgue space $L^p({{\mathbb R}^n\times{\mathbb R}^m})$ with some $p>1$ or the Hardy space $H^p({{\mathbb R}^n\times{\mathbb R}^m})$ with some $p\le1$ but near 1 to the Lebesgue space $L^q({{\mathbb R}^n\times{\mathbb R}^m})$ with some $q>1$.
Let $p\in(0, 1]$. In this paper, the authors prove that a sublinear operator $T$ (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces $H^p({{\mathbb R}^n\times{\mathbb R}^m})$ to some quasi-Banach space ${\mathcal B}$ if and only if $T$ maps all $(p, 2, s_1, s_2)$-atoms into uniformly bounded elements of ${\mathcal B}$. Here $s_1\ge\lfloor n(1/p-1)\rfloor$ and $s_2\ge\lfloor m(1/p-1)\rfloor$. As usual, $\lfloor n(1/p-1)\rfloor$ denotes the maximal integer no more than $n(1/p-1)$. Applying this result, the authors establish the boundedness of the commutators generated by Calder\'on-Zygmund operators and Lipschitz functions from the Lebesgue space $L^p({{\mathbb R}^n\times{\mathbb R}^m})$ with some $p>1$ or the Hardy space $H^p({{\mathbb R}^n\times{\mathbb R}^m})$ with some $p\le1$ but near 1 to the Lebesgue space $L^q({{\mathbb R}^n\times{\mathbb R}^m})$ with some $q>1$.
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DOI：
--
发表时间：
1980
期刊：
--
影响因子：
--
作者：
R. Coifman;R. Rochberg;M. Taibleson;G. Weiss
通讯作者：
R. Coifman;R. Rochberg;M. Taibleson;G. Weiss
影响因子：
0.6
作者：
F. Weisz
通讯作者：
F. Weisz
影响因子：
4.9
作者：
S. Chang;R. Fefferman
通讯作者：
S. Chang;R. Fefferman
影响因子：
1.2
作者：
R. Fefferman
通讯作者：
R. Fefferman
DOI：
10.5036/bfsiu1968.25.19
发表时间：
1993
期刊：
Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics
影响因子：
--
作者：
K. Yabuta
通讯作者：
K. Yabuta