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Boundedness of para-product operators on spaces of homogeneous type

Yayuan Xiao — 2017

Czechoslovak Mathematical Journal

We obtain the boundedness of Calderón-Zygmund singular integral operators $T$ of non-convolution type on Hardy spaces $H^{p} (𝒳)$ for $1 / (1 + ϵ) < p \leq 1$ , where $𝒳$ is a space of homogeneous type in the sense of Coifman and Weiss (1971), and $ϵ$ 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...

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