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Let $ω : (0, \infty) \to (0, \infty)$ be a gauge function satisfying certain mid regularity conditions. A (signed) finite Borel measure $μ \in ℝ^{n}$ is called $ω$ -Zygmund if there exists a positive constant $C$ such that $| μ (Q_{+}) - μ (Q_{-}) | \leq C ω (ℓ (Q_{+})) | Q_{+} |$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size. Similarly, $μ$ is called an $ω$ - symmetric measure if there exists a positive constant $C$ such that $| μ (Q_{+}) / μ (Q_{-}) - 1 | \leq C ω (ℓ (Q_{+}))$ for any pair $Q_{+}, Q_{-} \subset ℝ^{n}$ of adjacent cubes of the same size, $ℓ (Q_{+}) = ℓ (Q_{-}) < 1$ . We characterize Zygmund and symmetric measures in terms of their harmonic extensions. Also, we show that the quadratic condition...

Symmetric Harmonic Groups and Translation Invariant Dirichlet Spaces.

Gunnar Forst (1972)

Inventiones mathematicae

Symmetric reflected diffusions

E. Pardoux, R. J. Williams (1994)

Annales de l'I.H.P. Probabilités et statistiques

Symmetry and Overdetermined Boundary Value Problems.

Robert Molzon (1991)

Forum mathematicum

Symmetry for exterior elliptic problems and two conjectures in potential theory

Boyan Sirakov (2001)

Annales de l'I.H.P. Analyse non linéaire

Symmetry problems 2

N. S. Hoang, A. G. Ramm (2009)

Annales Polonici Mathematici

Some symmetry problems are formulated and solved. New simple proofs are given for some symmetry problems studied earlier. One of the results is as follows: if a single-layer potential of a surface, homeomorphic to a sphere, with a constant charge density, is equal to c/|x| for all sufficiently large |x|, where c > 0 is a constant, then the surface is a sphere.

Systèmes doublement orthogonaux de fonctions holomorphes et applications

Thanh Van Nguyen, Ahmed Zeriahi (1995)

Banach Center Publications

0. Introduction. Nous donnons ici une étude systématique des systèmes doublement orthogonaux "de Bergman" et leurs applications à certains aspects de l'analyse pluricomplexe: espaces de fonctions holomorphes, fonctions séparément analytiques. C'est en quelque sorte un article de synthèse. On y trouve cependant des démonstrations détaillées qui n'ont paru nulle part ailleurs.

Szegő projections for Hardy spaces of monogenic functions and applications.

Bernstein, Swanhild, Lanzani, Loredana (2002)

International Journal of Mathematics and Mathematical Sciences

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