Near-maximizers of Cauchy wavelet concentration are quantitatively close to hyperbolic balls and to reproducing kernels, with explicit constants uniform in the wavelet parameter.
Weighted contractivity for derivatives of functions in the Bergman space on the unit disk
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abstract
In a recent paper, Ramos and Tilli proved certain sharp inequality for analytic functions in subdomains of the unit disk. We will generalize their main inequality for derivatives of functions from Bergman space with respect to two diferent measures. Some connections with an analog for the Fock spaces, earlier investigated in Kalaj, will also be discussed.
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Uniform stability of concentration inequalities and applications
Near-maximizers of Cauchy wavelet concentration are quantitatively close to hyperbolic balls and to reproducing kernels, with explicit constants uniform in the wavelet parameter.