Tohoku Mathematical Journal
2004
September
SECOND SERIES VOL. 56, NO. 3

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

Title A CLASS OF MULTILINEAR OSCILLATORY SINGULAR INTEGRALS RELATED TO BLOCK SPACES

Author Shanzhen Lu and Huoxiong Wu

(Received January 15, 2002, revised March 23, 2004)
Abstract. This paper is devoted to the study on the $L^p$-mapping properties for a class of multilinear oscillatory singular integrals with polynomial phase and rough kernel. By means of the method of block decomposition for the kernel function, the authors show that for any non-trivial polynomial phase, the $L^p(\boldsymbol{R}^n)$ boundedness of the multilinear oscillatory singular integral operators and that of the corresponding local multilinear singular integral operators are equivalent; and for any real-valued polynomial phase, the $L^p(\boldsymbol{R}^n)$ boundedness of the multilinear oscillatory integral operators can be deduced from that of the corresponding multilinear singular integral operators.

2000 Mathematics Subject Classification. Primary 42B20; Secondary 42B25.

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