In this paper, we study the Marcinkiewicz integral operators MΩ,h on the product space Rn x Rm. We prove that MΩ,h is bounded on Lp(Rn x Rm) (1< p < ∞) provided that h is a bounded radial function and Ω is a function in certain block space Bq (0,0) (Sn−1 x Sm−1) for some q > 1. We also establish the optimality of our condition in the sense that the space Bq (0,0) (Sn−1 x Sm−1) cannot be replaced by Bq (0,r) (Sn−1 x Sm−1) for any −1 < r < 0. Our results improve some known results.
@article{urn:eudml:doc:41832,
title = {Rough Marcinkiewicz integral operators on product spaces.},
journal = {Collectanea Mathematica},
volume = {56},
year = {2005},
pages = {275-297},
zbl = {1091.42012},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41832}
}
Al-Qassem, Hussein M. Rough Marcinkiewicz integral operators on product spaces.. Collectanea Mathematica, Tome 56 (2005) pp. 275-297. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41832/