Marcinkiewicz integrals on product spaces

H. Al-Qassem, et al. "Marcinkiewicz integrals on product spaces." Studia Mathematica 167.3 (2005): 227-234. <http://eudml.org/doc/284761>.

@article{H2005,
abstract = {We prove the $L^\{p\}$ boundedness of the Marcinkiewicz integral operators $μ_\{Ω\}$ on $ℝ^\{n₁\}× ⋯ ×ℝ^\{n_\{k\}\}$ under the condition that $Ω ∈ L(log L)^\{k/2\}(^\{n₁-1\}× ⋯ ×^\{n_\{k\}-1\})$. The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.},
author = {H. Al-Qassem, A. Al-Salman, L. C. Cheng, Y. Pan},
journal = {Studia Mathematica},
keywords = {Marcinkiewicz integrals; product spaces; -boundedness},
language = {eng},
number = {3},
pages = {227-234},
title = {Marcinkiewicz integrals on product spaces},
url = {http://eudml.org/doc/284761},
volume = {167},
year = {2005},
}

TY - JOUR
AU - H. Al-Qassem
AU - A. Al-Salman
AU - L. C. Cheng
AU - Y. Pan
TI - Marcinkiewicz integrals on product spaces
JO - Studia Mathematica
PY - 2005
VL - 167
IS - 3
SP - 227
EP - 234
AB - We prove the $L^{p}$ boundedness of the Marcinkiewicz integral operators $μ_{Ω}$ on $ℝ^{n₁}× ⋯ ×ℝ^{n_{k}}$ under the condition that $Ω ∈ L(log L)^{k/2}(^{n₁-1}× ⋯ ×^{n_{k}-1})$. The exponent k/2 is the best possible. This answers an open question posed by Y. Ding.
LA - eng
KW - Marcinkiewicz integrals; product spaces; -boundedness
UR - http://eudml.org/doc/284761
ER -