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Boundedness of rough singular integral operators on homogeneous Herz spaces

Part of: Harmonic analysis in several variables Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Guoen Hu ,
Shanzhen Lu  and
Dachun Yang
Guoen Hu
Affiliation:
Department of Applied Mathematics, Institute of Information Engineering, Box 1001-47, Zhengzhou 450002, P. R. China
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China e-mail: lusz@bnu.edu.cn e-mail: dcyang@bnu.edu.cn
Dachun Yang
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China e-mail: lusz@bnu.edu.cn e-mail: dcyang@bnu.edu.cn
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Abstract

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The authors establish the boundedness on the Herz spaces and the weak Herz spaces for a large class of rough singular integral operators and their corresponding fractional versions. Applications are given to Fefferman's rough singular integral operators, their fractional versions, their commutators with BMO() functions and Ricci-Stein oscillatory singular integral operators. Some new results are obtained.

Keywords

Herz spaceLebesgue spacepower weightsingular integralfractional singular integral

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory 47A30: Norms (inequalities, more than one norm, etc.) 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 2 , April 1999 , pp. 201 - 223
Copyright
Copyright © Australian Mathematical Society 1999

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