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In , Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-
forms. Furthermore, B. Street in , and Stein and Street in [64–67] extended the theories of the
L p boundedness for multi-parameter singular integral operators, such as the Calderón Zygmund
operators and singular Radon transforms. In this dissertation, we will study the Hardy space H p
and its dual space associated with both the one-parameter and multi-parameter singular Radon
transforms, and consider the boundedness of the singular Radon transforms on such Hardy spaces
H p when 0 ≤ p ≤ 1.
Inspired by recent characterization of the Hardy spaces on product spaces, we will take advan-
tage of the discrete Littlewood-Paley analysis [14,32,43] to define the Hardy spaces H p and the
Carleson measure spaces CMO p associated with the multi-parameter singular Radon transforms.
Moreover, we will prove the H p boundedness of those operators and thus obtain the endpoint es-
timates for the L p boundedness of the singular Radon transforms by Christ, Nagel, Wainger and
Stein  and and for multi-parameter singular Radon transforms by Street and Stein [65–68].
Shen, Jiawei, "Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms" (2018). Wayne State University Dissertations. 1962.
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