A rough multiple Marcinkiewicz integral along continuous surfaces
Wu, Huoxiong
Tohoku Math. J. (2), Tome 59 (2007) no. 1, p. 145-166 / Harvested from Project Euclid
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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.
Publié le : 2007-05-14
Classification:  Marcinkiewicz integral,  continuous surface,  rough kernel,  block spaces,  product spaces,  Fourier transform estimate,  Littlewood-Paley theory,  42B20,  42B25,  42B99 
@article{1182180732,
     author = {Wu, Huoxiong},
     title = {A rough multiple Marcinkiewicz integral along continuous surfaces},
     journal = {Tohoku Math. J. (2)},
     volume = {59},
     number = {1},
     year = {2007},
     pages = { 145-166},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1182180732}
}

Wu, Huoxiong. A rough multiple Marcinkiewicz integral along continuous surfaces. Tohoku Math. J. (2), Tome 59 (2007) no. 1, pp.  145-166. http://gdmltest.u-ga.fr/item/1182180732/