Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 235-252, 2017
Boundedness of para-product operators on spaces of homogeneous type
Yayuan Xiao
Received October 8, 2015. First published February 24, 2017.
Abstract: We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^p(\mathcal X)$ for $ 1/{(1+\epsilon)}<p\le1$, where ${\mathcal X}$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $\epsilon$ is the regularity exponent of the kernel of the singular integral operator $T$. Our approach relies on the discrete Littlewood-Paley-Stein theory and discrete Calderón's identity. The crucial feature of our proof is to avoid atomic decomposition and molecular theory in contrast to what was used in the literature.
Keywords: boundedness; Calderón-Zygmund singular integral operator; para-product; spaces of homogeneous type
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Affiliations: Yayuan Xiao, Department of Mathematics, Ball State University, 2000 W University Ave, Muncie 47306, Indianapolis, USA, e-mail: yxiao3@bsu.edu
