Weak type $(1,1)$ estimates for Marcinkiewicz integrals with rough kernels
Fan, Dashan ; Sato, Shuichi
Tohoku Math. J. (2), Tome 53 (2001) no. 4, p. 265-284 / Harvested from Project Euclid
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We consider Marcinkiewicz integrals arising from rough kernels satisfying the $L\log L$ condition on the unit $(n-1)$-sphere and prove the weak type (1, 1) estimates. We also prove the weighted weak type (1, 1) estimates with certain $A_1$-weights. In this case the $L\log L$-condition is replaced by the $L^q$-condition with $q>1$.
Publié le : 2001-05-14
Classification:  Littlewood-Paley functions,  Marcinkiewicz integrals,  weak type estimates,  42B20 
@article{1178207481,
     author = {Fan, Dashan and Sato, Shuichi},
     title = {Weak type $(1,1)$ estimates for Marcinkiewicz integrals with rough kernels},
     journal = {Tohoku Math. J. (2)},
     volume = {53},
     number = {4},
     year = {2001},
     pages = { 265-284},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178207481}
}

Fan, Dashan; Sato, Shuichi. Weak type $(1,1)$ estimates for Marcinkiewicz integrals with rough kernels. Tohoku Math. J. (2), Tome 53 (2001) no. 4, pp.  265-284. http://gdmltest.u-ga.fr/item/1178207481/