Area functions characterizations of weighted Bergman spaces
نویسندگان
چکیده
منابع مشابه
New Characterizations of Bergman Spaces
We obtain several new characterizations for the standard weighted Bergman spaces Aα on the unit ball of C in terms of the radial derivative, the holomorphic gradient, and the invariant gradient.
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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...
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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...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2017
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2016.10.025