Abstract
AbstractThis paper is devoted to the study on the Lp ‐mapping properties for certain singular integral operators with rough kernels and related Littlewood–Paley functions along “polynomial curves” on product spaces ℝm × ℝn (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 Lp (ℝm × ℝn ), 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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