On multilinear oscillatory singular integrals with rough kernels
نویسندگان
چکیده
منابع مشابه
On Multilinear Oscillatory Integrals, Nonsingular and Singular
Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L norm inequalities are established for multilinear integral operators of Calderón-Zygmund type which incorporate oscillatory factors e iP , where P is a real-valued polynomial. A related problem concerning upper bounds for measures of sublevel sets is solved.
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Sn−1 Ω = 0. The radial factor h has bounded variation. The necessary condition on the weight is similar to the Ap condition but involves rectangles (instead of cubes) arising from a covering of a star-shaped set related to Ω. AMS Mathematics Subject Classification: 42B20
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Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).
متن کاملMultilinear Calderón–zygmund Singular Integrals
This paper contains the material covered in a minicourse given by the author at the Centre de Recerca Matemàtica in Barcelona during the period May 4–9, 2009. The course was an expanded version of a series of three lectures delivered by the author two weeks earlier (April 23–25) at the New Mexico Analysis Seminar held at the University of New Mexico in Albuquerque. The author would like to than...
متن کاملMultiple Weighted Norm Inequalities for Maximal Multilinear Singular Integrals with Non-Smooth Kernels
Weighted norm inequalities for maximal truncated operators of multilinear singular integrals with non-smooth kernels in the sense of Duong, Grafakos, and Yan are obtained; this class of operators extends the class of multilinear CalderónZygmund operators introduced by Coifman and Meyer and includes the higher order commutators of Calderón. The weighted norm inequalities obtained in this work ar...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2004
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2004.03.035