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A CLASS OF MULT1LINEAR OSCILLATORY SINGULAR INTEGRALS RELATED TO BLOCK SPACES

陆善镇SHANZHEN LU AND HUOXIONG WU

Tohoku Math. J. 56 (2004). 299-315,-0001,():

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摘要/描述

This paper is devoted to the study on the LP -mapping prnperlies for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel By means of the method of block decomposition tot the kernel funcion. the authors show that for any non trivial polynomial phase, the Lp(Rn) boundedness of the muhilinear oseillatory singular integral operators and that of the corresponding local multilinear singular integral opterators are equivalent; and for any real-valued polynomial phase, the Lp(Rn) bonundedness of the multi linear oscillatory integral operators can be deduced from that of the cprresponding multilinear singular integral operators.

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