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The diagonal mapping in mixed norm spaces

Tom 163 / 2004

Guangbin Ren, Jihuai Shi Studia Mathematica 163 (2004), 103-117 MSC: 32A37, 47B38. DOI: 10.4064/sm163-2-1

Streszczenie

For any holomorphic function $F$ in the unit polydisc $U^n$ of ${\mathbb C}^n$, we consider its restriction to the diagonal, i.e., the function in the unit disc $U$ of $\mathbb C$ defined by ${\mathcal D}F(z)=F(z,\dots,z)$, and prove that the diagonal mapping ${\mathcal D}$ maps the mixed norm space $H^{p, q, \alpha}(U^n)$ of the polydisc onto the mixed norm space $H^{p,q,|\alpha|+(p/q+1)(n-1)}(U)$ of the unit disc for any $0< p< \infty$ and $0< q\le\infty$.

Autorzy

  • Guangbin RenDepartment of Mathematics
    University of Science and Technology of China
    Hefei, Anhui 230026, P.R. China
    and
    Department of Mathematics
    University of Aveiro
    3810-193 Aveiro, Portugal
    E-mail: ren@mat.ua.pt
    e-mail
  • Jihuai ShiDepartment of Mathematics
    University of Science and Technology of China
    Hefei, Anhui 230026, P.R. China
    e-mail

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