Singular integrals on Carleson measure spaces 𝐶𝑀𝑂^{𝑝} on product spaces of homogeneous type

Li, Ji; Ward, Lesley

doi:10.1090/S0002-9939-2013-11604-7

Singular integrals on Carleson measure spaces $\textrm {CMO}^p$ on product spaces of homogeneous type
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by Ji Li and Lesley A. Ward PDF

Proc. Amer. Math. Soc. 141 (2013), 2767-2782 Request permission

Abstract:

In the setting of product spaces $\widetilde {M}$ of homogeneous type, we prove that every product non-isotropic smooth (NIS) operator $T$ is bounded on the generalized Carleson measure space $\textrm {CMO}^p(\widetilde {M})$ of Han, Li and Lu for $p_0 < p < 1$. Here $p_0$ depends on the homogeneous dimensions of the measures on factors of the product space $\widetilde {M}$ and on the regularity of the quasi-metrics on factors of $\widetilde {M}$. The $L^p$ boundedness for $1<p<\infty$ of the class of NIS operators was developed in both the one-parameter case and the multiparameter case by Nagel and Stein, and the $H^p$ boundedness was established in the multiparameter case by Han, Li and Lu.

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