Marcinkiewicz integrals on product spaces
Volume 167 / 2005
Studia Mathematica 167 (2005), 227-234
MSC: Primary 42B20; Secondary 42B25.
DOI: 10.4064/sm167-3-4
Abstract
We prove the $L^p$ boundedness of the Marcinkiewicz integral operators $\mu_{\mit\Omega}$ on ${\mathbb R}^{n_1}\times\cdots\times{\mathbb R}^{n_k}$ under the condition that ${\mit\Omega} \in L (\log L)^{k/2}({\mathbb S}^{n_1 -1}\times\cdots\times{\mathbb S}^{n_k-1})$. The exponent $k/2$ is the best possible. This answers an open question posed by Y. Ding.
