Zeros of functions in weighted Bergman spaces.
نویسندگان
چکیده
منابع مشابه
Zeros of Extremal Functions in Weighted Bergman Spaces
For −1 < α ≤ 0 and 0 < p < ∞, the solutions of certain extremal problems are known to act as contractive zerodivisors in the weighted Bergman space Aα. We show that for 0 < α ≤ 1 and 0 < p < ∞, the analogous extremal functions do not have any extra zeros in the unit disk and, hence, have the potential to act as zero-divisors. As a corollary, we find that certain families of hypergeometric funct...
متن کاملZeros of random functions in Bergman spaces
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متن کاملWeighted composition operators on weighted Bergman spaces and weighted Bloch spaces
In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.
متن کاملOperators on weighted Bergman spaces
Let ρ : (0, 1] → R+ be a weight function and let X be a complex Banach space. We denote by A1,ρ(D) the space of analytic functions in the disc D such that ∫ D |f(z)|ρ(1 − |z|)dA(z) < ∞ and by Blochρ(X) the space of analytic functions in the disc D with values in X such that sup|z|<1 1−|z| ρ(1−|z|)‖F ′(z)‖ < ∞. We prove that, under certain assumptions on the weight, the space of bounded operator...
متن کاملCanonical Divisors in Weighted Bergman Spaces
Canonical divisors in Bergman spaces can be found as solutions of extremal problems. We derive a formula for certain extremal functions in the weighted Bergman spaces Aα for α > −1 and 1 ≤ p <∞. This leads to a study of the zeros of a specific family of hypergeometric functions.
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1977
ISSN: 0026-2285
DOI: 10.1307/mmj/1029001887