Families of fractional Fantappie transforms

Authors

  • Evgueni Doubtsov

Keywords:

fractional Fantappie transform, pointwise multiplier

Abstract

Let $B_n$ denote the unit ball in ${\mathbb C}^n$, $n\ge 1$. Given an $\alpha>0$, let ${\mathcal F}_\alpha(n)$ denote the class of functions defined for $z\in B_n$ by integrating the kernel $(1-\langle z, w \rangle)^{-\alpha}$ against a complex Borel measure $d\mu(w)$, $w\in B_n$. The family ${\mathcal F}_0(n)$ corresponds to the logarithmic kernel $\log(1/(1-\langle z, w \rangle))$. Various properties of the spaces ${\mathcal F}_\alpha(n)$, $\alpha\ge 0$, are obtained. In particular, pointwise multiplies for ${\mathcal F}_\alpha(n)$ are investigated. doi:10.1017/S0004972710000031

Published

2010-09-22

Issue

Vol. 82 (2010)

Section

Articles
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