Abstract
By means of the method of block decompositions for kernel functions and some delicate estimates on Fourier transforms, the $L^p(\boldsymbol{R}^m\times\boldsymbol{R}^n\times\boldsymbol{R})$-boundedness of the multiple Marcinkiewicz integral is established along a continuous surface with rough kernel for some $p>1$. The condition on the integral kernel is the best possible for the $L^2$-boundedness of the multiple Marcinkiewicz integral operator.
Citation
Huoxiong Wu. "A rough multiple Marcinkiewicz integral along continuous surfaces." Tohoku Math. J. (2) 59 (2) 145 - 166, 2007. https://doi.org/10.2748/tmj/1182180732
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