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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

$H^ p$- and $L^ p$-variants of multiparameter Calder贸n-Zygmund theory


Authors: Anthony Carbery and Andreas Seeger
Journal: Trans. Amer. Math. Soc. 334 (1992), 719-747
MSC: Primary 42B30; Secondary 42B15, 42B20
DOI: https://doi.org/10.1090/S0002-9947-1992-1072104-4
MathSciNet review: 1072104
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Abstract: We consider Calder贸n-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鈥 results on ${L^p}$-variants of Calder贸n-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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Keywords: Calder&#243;n-Zygmund theory, product spaces
Article copyright: © Copyright 1992 American Mathematical Society