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A problem on rough parametric Marcinkiewicz functions

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  09 April 2009

Yong Ding ,
Shanzhen Lu  and
Kôzô Yabuta
Yong Ding
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing, 100875, P. R., China e-mail: dingy@bnu.edu.cn e-mail: lusz@bnu.edu.cn
Shanzhen Lu
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing, 100875, P. R., China e-mail: dingy@bnu.edu.cn e-mail: lusz@bnu.edu.cn
Kôzô Yabuta
Affiliation:
School of Science, Kwansei Gakuin University, Uegahara 1-1-155, Nishinomiya 662-8501Japan e-mail: yabuta@kwansei.ac.jp
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Abstract

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In this note the authors give the L2(n) boundedness of a class of parametric Marcinkiewicz integral with kernel function Ω in L log+L(Sn−1) and radial function h(|x|) ∈ l ∞ l(Lq)(+) for 1 < q ≦.

As its corollary, the Lp (n)(2 < p < ∞) boundedness of and and with Ω in L log+L (Sn-1) and h(|x|) ∈ l∞ (Lq)(+) are also obtained. Here and are parametric Marcinkiewicz functions corresponding to the Littlewood-Paley g*λ-function and the Lusin area function S, respectively.

Keywords

Marcinkiewicz integralLittlewood-Paley g-functionLusin area integralrough kernel

MSC classification

Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 13 - 22
Copyright
Copyright © Australian Mathematical Society 2002

References

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