Weighted Bergman spaces and the integral means spectrum of conformal mappings

DOI10.1215/S0012-7094-04-12725-3zbMath1075.30005arXivmath/0406345OpenAlexW2021730697WikidataQ59288492 ScholiaQ59288492MaRDI QIDQ1781953

Serguei Shimorin, Haakan Hedenmalm

Publication date: 9 June 2005

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0406345

zbMATH Keywords

Bergman spacesintegral means spectrumarea-type estimates

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Capacity and harmonic measure in the complex plane (30C85) Bergman spaces of functions in several complex variables (32A36) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Kernel functions in one complex variable and applications (30C40)

Related Items (27)

Branching points area theorems for univalent functions ⋮ Spectral estimates of the \(p\)-Laplace Neumann operator in conformal regular domains ⋮ On \(L^1\)-estimates of derivatives of univalent rational functions ⋮ An estimate of the universal means spectrum of conformal mappings ⋮ Weighted integrability of polyharmonic functions ⋮ Norm expansion along a zero variety ⋮ On means with power $-2$ for the dervatives of functions of class $S$ ⋮ Brennan's conjecture and universal Sobolev inequalities ⋮ Three Problems in Function Theory ⋮ Spectral notions for conformal maps: a survey ⋮ On Hörmander's solution of the \(\bar{\partial}\)-equation. I ⋮ Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian ⋮ Boundary properties of Green functions in the plane ⋮ Bloch functions and asymptotic tail variance ⋮ A conformal mapping example ⋮ The solution operator of the inhomogeneous Dirichlet problem in the unit ball ⋮ Random conformal snowflakes ⋮ Spectral estimates of the \(p\)-Laplace Neumann operator and Brennan's conjecture ⋮ Lower estimates for integral means of univalent functions ⋮ Nevanlinna domains with large boundaries ⋮ Spectral properties of the Neumann-Laplace operator in quasiconformal regular domains ⋮ Gaussian analytic functions and operator symbols of Dirichlet type ⋮ Harmonic measure and SLE ⋮ WEIGHTED ESTIMATES ON FRACTAL DOMAINS ⋮ On the exceptional set in a conditional theorem of Littlewood ⋮ On the Makarov law of the iterated logarithm ⋮ On the universal integral means spectrum of conformal mappings near the origin

Cites Work

• On coefficient problems for univalent functions and conformal dimension
• Estimates on integral means of the derivatives of univalent functions
• Some results connected with Brennan's conjecture
• The dual of a Bergman space on simply connected domains.
• A problem in prediction theory
• Inequalities for the coefficients of univalent functions
• Experimental bounds for the universal integral means spectrum of conformal maps
• Theory of Reproducing Kernels
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