Weighted Boundedness of Maximal Functions and Fractional Bergman Operators
نویسندگان
چکیده
منابع مشابه
Boundedness and compactness of weighted composition operators between weighted Bergman spaces
We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.
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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 $mathbb{C}^n$.
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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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Let ρ be a weight function, let X be a complex Banach space and let Bρ denote the space of analytic functions in the disc D such that R 1 0 ρ(1 − r)M1(f ′, r) dr < ∞, we prove that, under certain assumptions on the weight, the space of bounded operators L(Bρ,X) is isometrically isomorphic to the space Λρ(X) of X-valued analytic functions such that ‖F ′(z)‖ = O ρ(1−|z|) 1−|z| . Several applicati...
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For a smoothly bounded strictly pseudoconvex domain, we describe the boundary singularity of weighted Bergman kernels with respect to weights behaving like a power (possibly fractional) of a defining function, and, more generally, of the reproducing kernels of Sobolev spaces of holomorphic functions of any real order. This generalizes the classical result of Fefferman for the unweighted Bergman...
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2017
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-017-9881-5