Open Access
January, 2010 Boundedness of sublinear operators on product Hardy spaces and its application
Der-Chen CHANG, Dachun YANG, Yuan ZHOU
J. Math. Soc. Japan 62(1): 321-353 (January, 2010). DOI: 10.2969/jmsj/06210321

Abstract

Let p ( 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 ( R n × R m ) to some quasi-Banach space B if and only if T maps all ( p , 2 , s 1 , s 2 ) -atoms into uniformly bounded elements of B . Here s 1 n ( 1 / p - 1 ) and s 2 m ( 1 / p - 1 ) . As usual, n ( 1 / p - 1 ) denotes the maximal integer no more than n ( 1 / p - 1 ) . Applying this result, the authors establish the boundedness of the commutators generated by Calderón-Zygmund operators and Lipschitz functions from the Lebesgue space L p ( R n × R m ) with some p > 1 or the Hardy space H p ( R n × R m ) with some p 1 but near 1 to the Lebesgue space L q ( R n × R m ) with some q > 1 .

Citation

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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

Information

Published: January, 2010
First available in Project Euclid: 5 February 2010

zbMATH: 1195.42060
MathSciNet: MR2648225
Digital Object Identifier: 10.2969/jmsj/06210321

Subjects:
Primary: 42B20
Secondary: 42B25 , 42B30 , 47B47

Keywords: Calderón-Zygmund operator , commutator , Hardy space , Lebesgue space , Lipschitz function , product space , sublinear operator

Rights: Copyright © 2010 Mathematical Society of Japan

Vol.62 • No. 1 • January, 2010
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