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.

Yayuan Xiao, Department of Mathematics, Ball State University, 2000 W University Ave, Muncie 47306, Indianapolis, USA, e-mail: yxiao3@bsu.edu

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

Classification (MSC 2010): 42B25, 42B30

DOI: 10.21136/CMJ.2017.0536-15

Full text available as PDF.


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