L p -Boundedness of Marcinkiewicz Integrals with Hardy Space Function Kernels

Springer Science and Business Media LLC - 2000
Yong Ding1, Dashan Fan2, Yibiao Pan3
1Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China
2Department of Mathematics, Anhui University and University of Wisconsin-Milwaukee, Wisconsin MW 53201, USA
3Department of Mathematics, University of Pittsburgh, Pittsburgh, USA

Tóm tắt

We give the L p -boundedness for a class of Marcinkiewicz integral operators $$ \mu _{\Omega } ,\mu ^{ * }_{{\Omega ,\lambda }} $$ and μΩ,s related to the Littlewood-Paley g-function, $$ g^{ * }_{\lambda } $$ -function and the area integral S, respectively. These operators have the kernel functions Ω∈H 1 (S n−1), the Hardy space on S n−1. These results in this paper substantially improve and extend the known results.

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Tài liệu tham khảo

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