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General Littlewood–Paley functions and singular integral operators on product spaces
Author(s) -
Wu Huoxiong
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310369
Subject(s) - mathematics , singular integral , singular integral operators , bounded function , product (mathematics) , kernel (algebra) , pure mathematics , fourier integral operator , polynomial , fourier transform , singular integral operators of convolution type , operator theory , mathematical analysis , microlocal analysis , integral equation , geometry
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)