Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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A DOUBLE INTEGRAL CHARACTERIZATION OF A BERGMAN TYPE SPACE AND ITS MÖBIUS INVARIANT SUBSPACE

  • Yuan, Cheng (School of Applied Mathematics Guangdong University of Technology) ;
  • Zeng, Hong-Gang (School of Mathematics Tianjin University)
  • Received : 2019.01.14
  • Accepted : 2019.04.25
  • Published : 2019.11.30
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Abstract

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.

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References

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