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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$H^ p$- and $L^ p$-variants of multiparameter Calder贸n-Zygmund theory
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by Anthony Carbery and Andreas Seeger PDF
Trans. Amer. Math. Soc. 334 (1992), 719-747 Request permission

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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Additional Information
  • © Copyright 1992 American Mathematical Society
  • 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