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Hardy Space Theory And Endpoint Estimates For Multi-Parameter Singular Radon Transforms, Jiawei Shen

Wayne State University Dissertations

In [12], Christ, Nagel, Stein and Waigner studied the L p theories for the singular Radon Trans-

forms. Furthermore, B. Street in [68], 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 …