Hardy Space Theory And Endpoint Estimates For Multi Parameter Singular Radon Transforms
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Hardy Space Theory and Endpoint Estimates for Multi-parameter Singular Radon Transforms
Author | : Jiawei Shen |
Publisher | : |
Total Pages | : 119 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : |
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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 [640́367] extended the theories of the L p boundedness for multi-parameter singular integral operators, such as the Calder©đn 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 9́Þ p 9́Þ 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 [12] and and for multi-parameter singular Radon transforms by Street and Stein [650́368].
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