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Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces H... and N*.

Manfred Stoll (1976)

Journal für die reine und angewandte Mathematik

Hölder continuity of proper holomorphic mappings

François Berteloot (1991)

Studia Mathematica

We prove the Hölder continuity for proper holomorphic mappings onto certain piecewise smooth pseudoconvex domains with "good" plurisubharmonic peak functions at each point of their boundaries. We directly obtain a quite precise estimate for the exponent from an attraction property for analytic disks. Moreover, this way does not require any consideration of infinitesimal metric.

Hölder continuous solutions to Monge–Ampère equations

Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)

Journal of the European Mathematical Society

Let $(X, ω)$ be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on $X$ with $L^{p}$ right hand side, $p > 1$ . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range $(X, ω)$ of the complex Monge-Ampère operator acting on $ω$ -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with $L^{p}$ -density belong to $(X, ω)$ and proving that $(X, ω)$ has the...

Holomorphe Funktionen auf Gebieten über Banach-Räumen zu vorgegebenen Konvergenzradien.

Martin Schottenloher (1977)

Manuscripta mathematica

Holomorphic convexity of spaces of analytic cycles

François Norguet, Yum-Tong Siu (1977)

Bulletin de la Société Mathématique de France

Holomorphic mapping of annuli in $C^{n}$ and the associated extremal function

Eric Bedford, Dan Burns (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Homogeneous extremal function for a ball in ℝ²

Mirosław Baran (1999)

Annales Polonici Mathematici

We point out relations between Siciak’s homogeneous extremal function $Ψ_{B}$ and the Cauchy-Poisson transform in case $B$ is a ball in ℝ². In particular, we find effective formulas for $Ψ_{B}$ for an important class of balls. These formulas imply that, in general, $Ψ_{B}$ is not a norm in ℂ².