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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ H\sp p$- and $ L\sp p$-variants of multiparameter Calderón-Zygmund theory


Authors: Anthony Carbery and Andreas Seeger
Journal: Trans. Amer. Math. Soc. 334 (1992), 719-747
MSC: Primary 42B30; Secondary 42B15, 42B20
MathSciNet review: 1072104
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Abstract: We consider Calderón-Zygmund operators on product domains. Under certain weak conditions on the kernel a singular integral operator can be proved to be bounded on $ {H^p}(\mathbb{R} \times \mathbb{R} \times \cdots \times \mathbb{R}), 0 < p \leq 1$, if its behaviour on $ {L^2}$ and on certain scalar-valued and vector-valued rectangle atoms is known. Another result concerns an extension of the authors' results on $ {L^p}$-variants of Calderón-Zygmund theory [1,23] to the product-domain-setting. As an application, one obtains estimates for Fourier multipliers and pseudo-differential operators.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1072104-4
PII: S 0002-9947(1992)1072104-4
Keywords: Calderón-Zygmund theory, product spaces
Article copyright: © Copyright 1992 American Mathematical Society