Boundedness of para-product operators on spaces of homogeneous type

摘要

  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)}ple1$, 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.