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$C^{\infty}$ approximations of convex, subharmonic, and plurisubharmonic functions

R. E. Greene, H. Wu (1979)

Annales scientifiques de l'École Normale Supérieure

Carleson measures for weighted harmonic mixed norm spaces on bounded domains in $ℝ^{n}$

Ivana Savković (2022)

Czechoslovak Mathematical Journal

We study weighted mixed norm spaces of harmonic functions defined on smoothly bounded domains in $ℝ^{n}$ . Our principal result is a characterization of Carleson measures for these spaces. First, we obtain an equivalence of norms on these spaces. Then we give a necessary and sufficient condition for the embedding of the weighted harmonic mixed norm space into the corresponding mixed norm space.

Cauchy-Szegö integrals for systems of harmonic functions

Adam Korányi, Stephen Vági (1972)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Characterization of best harmonic and superharmonic L1-approximations.

D.H. Armitage, S.J. Gardiner, W. Haussmann, ... (1996)

Journal für die reine und angewandte Mathematik

Choquetova teorie a Dirichletova úloha

Jaroslav Lukeš, Ivan Netuka, Jiří Veselý (2000)

Pokroky matematiky, fyziky a astronomie

Classes de Bergman de fonctions harmoniques

Jacqueline Detraz (1981)

Bulletin de la Société Mathématique de France

Comparisons of kernel functions boundary Harnack principle and relative Fatou theorem on Lipschitz domains

Jang-Mei G. Wu (1978)

Annales de l'institut Fourier

On a Lipschitz domain $D$ in $R^{n}$ , three theorems on harmonic functions are proved. The first (boundary Harnack principle) compares two positive harmonic functions at interior points near an open subset of the boundary where both functions vanish. The second extends some familiar geometric facts about the Poisson kernel on a sphere to the Poisson kernel on $D$ . The third theorem, on non-tangential limits of quotient of two positive harmonic functions in $D$ , generalizes Doob’s relative Fatou theorem on a...

Comportement non-tangentiel et comportement brownien des fonctions harmoniques dans un demi-espace. Démonstration probabiliste d'un théorème de Calderon et Stein

Jean Brossard (1978)

Séminaire de probabilités de Strasbourg

Cones of Lower Semicontinuous Functions and a Characterisation of Finely Hyperharmonic Functions.

Terry J. Lyons (1982)

Mathematische Annalen

Continuation of positive, closed currents and analytic sets.

Manfred Rapp (1993)

Mathematische Zeitschrift

Convergence in nonisotropic regions of harmonic functions in $^{n}$

Carme Cascante, Joaquin Ortega (1999)

Studia Mathematica

We study the boundedness in $L^{p} (^{n})$ of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in $L^{p} (^{n})$ with spectrum included in these horizontal strips.

Corrigendum to the paper "On the reproducing kernel for harmonic functions and the space of Bloch harmonic functions on the unit ball in R^{n}" (Studia Mathematica 87 (1987), 23-32)

Ewa Ligocka (1992)