Calderón–Zygmund operators on product Hardy spaces

By Yongsheng Han, Ming-Yi Lee, Chin-Cheng Lin, Ying-Chieh Lin. 2010

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Let T be a product Calderon–Zygmund singular integral introduced by Journe. Using an elegant rectangle atomic decomposition of Hp(Rn×Rm) and Journe's geometric covering lemma, R. Fefferman proved the remarkable Hp(Rn×Rm)−Lp(Rn×Rm) boundedness of T. In this paper we apply vector-valued singular integral, Calderon's identity, Littlewood–Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journe's covering lemma to show that T is bounded on product Hp(Rn×Rm) for max{nn+e,mm+e}<p⩽1 if and only if T1∗(1)=T2∗(1)=0, where e is the regularity exponent of the kernel of T.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/37f5f7461431346d036590e79aa29ed509c7d0d5