Rough Marcinkiewicz integral operators on product spaces.

Al-Qassem, Hussein M.. "Rough Marcinkiewicz integral operators on product spaces.." Collectanea Mathematica 56.3 (2005): 275-297. <http://eudml.org/doc/41832>.

@article{Al2005,
abstract = {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&lt; p &lt; ∞) 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 &gt; 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 &lt; r &lt; 0. Our results improve some known results.},
author = {Al-Qassem, Hussein M.},
journal = {Collectanea Mathematica},
keywords = {Análisis de Fourier; Operadores integrales; Integrales singulares; Acotación; Espacios LP; Marcinkiewicz integral operator; rough kernel; product space; block space},
language = {eng},
number = {3},
pages = {275-297},
title = {Rough Marcinkiewicz integral operators on product spaces.},
url = {http://eudml.org/doc/41832},
volume = {56},
year = {2005},
}

TY - JOUR
AU - Al-Qassem, Hussein M.
TI - Rough Marcinkiewicz integral operators on product spaces.
JO - Collectanea Mathematica
PY - 2005
VL - 56
IS - 3
SP - 275
EP - 297
AB - 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&lt; p &lt; ∞) 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 &gt; 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 &lt; r &lt; 0. Our results improve some known results.
LA - eng
KW - Análisis de Fourier; Operadores integrales; Integrales singulares; Acotación; Espacios LP; Marcinkiewicz integral operator; rough kernel; product space; block space
UR - http://eudml.org/doc/41832
ER -