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Title: Boundedness of para-product operators on spaces of homogeneous type (English)
Author: Xiao, Yayuan
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 67
Issue: 1
Year: 2017
Pages: 235-252
Summary lang: English
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Category: math
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Summary: 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\le 1$, 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. (English)
Keyword: boundedness
Keyword: Calderón-Zygmund singular integral operator
Keyword: para-product
Keyword: spaces of homogeneous type
MSC: 42B25
MSC: 42B30
idZBL: Zbl 06738515
idMR: MR3633009
DOI: 10.21136/CMJ.2017.0536-15
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Date available: 2017-03-13T12:10:32Z
Last updated: 2020-01-05
Stable URL: http://hdl.handle.net/10338.dmlcz/146051
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