Weighted integral representations of entire functions of several complex variables (Q935556)

Let \(H_{s, \gamma}^p ({\mathbb C^n})\) be the space of all entire functions \(f(z), z \in {\mathbb C^n}\) such that \[ \int_{\mathbb R^n} \left (\int_{\mathbb R^n} | f (x + i y)| ^p d x \right )^s | y| ^{\alpha} e^{- \sigma | y| ^{\rho}} \,d y < + \infty. \] Here \(n > 1, 1 \leq p \leq 2, 0 < s, \sigma < \infty, 1 < \rho < \infty, \alpha > - n.\) The author establishes (Theorem 1.1) integral representations for the functions of these spaces for the case \[ \frac{1}{p} < s, \frac{ps}{ps - 1} < 2^\rho. \] He obtains an explicit form and an estimate for reproducing kernels of these representations.