# Rough Marcinkiewicz integral operators on product spaces.

Collectanea Mathematica (2005)

- Volume: 56, Issue: 3, page 275-297
- ISSN: 0010-0757

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topAl-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< 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.},

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< 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.

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 -

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