Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 62, Number 1 (2010), 321-353.
Boundedness of sublinear operators on product Hardy spaces and its application
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 .
J. Math. Soc. Japan, Volume 62, Number 1 (2010), 321-353.
First available in Project Euclid: 5 February 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B30: $H^p$-spaces 42B25: Maximal functions, Littlewood-Paley theory 47B47: Commutators, derivations, elementary operators, etc.
CHANG, Der-Chen; YANG, Dachun; ZHOU, Yuan. Boundedness of sublinear operators on product Hardy spaces and its application. J. Math. Soc. Japan 62 (2010), no. 1, 321--353. doi:10.2969/jmsj/06210321. https://projecteuclid.org/euclid.jmsj/1265380433