Acta mathematica scientia, Series B >
ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES
Received date: 2009-02-10
Revised date: 2011-04-15
Online published: 2011-09-20
Supported by
Supported by the NSFC (10771054, 10971141, 11071200) and the NFS of Beijing (1092004) and the NFS of Fujian Province (2010J01013).
In this paper, the authors study the mapping properties of singular integrals on product domains with kernels in L(log+L)ε(Sm−1
× Sn−1) (ε = 1 or 2) supported by hyper-surfaces. The Lp bounds for such singular integral operators as well as the related
Marcinkiewicz integral operators are established, provided that the lower dimensional max-imal function is bounded on Lq(R3) for all q > 1. The condition on the integral kernels is known to be optimal.
DENG Liu-Rui , LI Zhong-Kai , MA Bo-Lin , WU Huo-Xiong . ROUGH MULTIPLE SINGULAR INTEGRALS ALONG HYPERSURFACES[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 2081 -2098 . DOI: 10.1016/S0252-9602(11)60383-4
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