Abstract
Let . In this paper, the authors prove that a sublinear operator (which is originally defined on smooth functions with compact support) can be extended as a bounded sublinear operator from product Hardy spaces to some quasi-Banach space if and only if maps all -atoms into uniformly bounded elements of . Here and . As usual, denotes the maximal integer no more than . Applying this result, the authors establish the boundedness of the commutators generated by Calderón-Zygmund operators and Lipschitz functions from the Lebesgue space with some or the Hardy space with some but near 1 to the Lebesgue space with some .
Citation
Der-Chen CHANG. Dachun YANG. Yuan ZHOU. "Boundedness of sublinear operators on product Hardy spaces and its application." J. Math. Soc. Japan 62 (1) 321 - 353, January, 2010. https://doi.org/10.2969/jmsj/06210321
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