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Littlewood–Paley $g$-functions with rough kernels on homogeneous groups

Tom 195 / 2009

Yong Ding, Xinfeng Wu Studia Mathematica 195 (2009), 51-86 MSC: Primary 42B25; Secondary 43A80, 43A99. DOI: 10.4064/sm195-1-4

Streszczenie

Let $\mathbb G$ be a homogeneousgroup on ${\mathbb R}^n$ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with $L\log^+\!\!L$ function kernel on $\gg$ is both of type $(p,p)$ and of weak type $(1,1)$. In this paper, the same results are proved for the Littlewood–Paley $g$-functions on $\mathbb G$

Autorzy

  • Yong DingSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics
    and Complex Systems (BNU)
    Beijing, 100875, China
    e-mail
  • Xinfeng WuDepartment of Mathematics
    China University of Mining
    and Technology (Beijing)
    Beijing, 100083, China
    e-mail

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