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General Littlewood–Paley functions and singular integral operators on product spaces

✍ Scribed by Huoxiong Wu

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
215 KB
Volume
279
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper is devoted to the study on the L^p^ ‐mapping properties for certain singular integral operators with rough kernels and related Littlewood–Paley functions along “polynomial curves” on product spaces ℝ^m^ × ℝ^n^ (m ≥ 2, n ≥ 2). By means of the method of block decomposition for kernel functions and some delicate estimates on Fourier transforms, the author proves that the singular integral operators and Littlewood–Paley functions are bounded on L^p^ (ℝ^m^ × ℝ^n^ ), p ∈ (1, ∞), and the bounds are independent of the coefficients of the polynomials. These results essentially improve or extend some well‐known results. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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