All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 6 Next

Displaying 101 – 120 of 162

Showing per page

An embedding relation for bounded mean oscillation on rectangles

Benoît F. Sehba (2014)

Annales Polonici Mathematici

In the two-parameter setting, we say a function belongs to the mean little BMO if its mean over any interval and with respect to any of the two variables has uniformly bounded mean oscillation. This space has been recently introduced by S. Pott and the present author in relation to the multiplier algebra of the product BMO of Chang-Fefferman. We prove that the Cotlar-Sadosky space b m o ( N ) of functions of bounded mean oscillation is a strict subspace of the mean little BMO.

An energy estimate for the complex Monge-Ampère operator

Urban Cegrell, Leif Persson (1997)

Annales Polonici Mathematici

We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.

An example for the holomorphic sectional curvature of the Bergman metric

Żywomir Dinew (2010)

Annales Polonici Mathematici

We study the behaviour of the holomorphic sectional curvature (or Gaussian curvature) of the Bergman metric of planar annuli. The results are then utilized to construct a domain for which the curvature is divergent at one of its boundary points and moreover the upper limit of the curvature at that point is maximal possible, equal to 2, whereas the lower limit is -∞.

An extension of Schwick's theorem for normal families

Yasheng Ye, Xuecheng Pang, Liu Yang (2015)

Annales Polonici Mathematici

In this paper, the definition of the derivative of meromorphic functions is extended to holomorphic maps from a plane domain into the complex projective space. We then use it to study the normality criteria for families of holomorphic maps. The results obtained generalize and improve Schwick's theorem for normal families.

An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki, Peter Pflug (2003)

Annales Polonici Mathematici

Let D j ⊂ ℂ k j be a pseudoconvex domain and let A j ⊂ D j be a locally pluriregular set, j = 1,...,N. Put X : = ⋃ j = 1 N A ₁ × . . . × A j - 1 × D j × A j + 1 × . . . × A N ⊂ ℂ k ₁ + . . . + k N . Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the “envelope of holomorphy” X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with f ̂ | X ∖ M = f . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].

An integral formula on submanifolds of domains of Cn..

Telemachos Hatziafratis (1991)

Publicacions Matemàtiques

A Bochner-Martinelli-Koppelman type integral formula on submanifolds of pseudoconvex domains in Cn is derived; the result gives, in particular, integral formulas on Stein manifolds.

Analytic disks with boundaries in a maximal real submanifold of 𝐂 2

Franc Forstneric (1987)

Annales de l'institut Fourier

Let M be a two dimensional totally real submanifold of class C 2 in C 2 . A continuous map F : Δ ‾ → C 2 of the closed unit disk Δ ‾ ⊂ C into C 2 that is holomorphic on the open disk Δ and maps its boundary b Δ into M is called an analytic disk with boundary in M . Given an initial immersed analytic disk F 0 with boundary in M , we describe the existence and behavior of analytic disks near F 0 with boundaries in small perturbations of M in terms of the homology class of the closed curve F 0 ( b Δ ) in M . We also prove a regularity theorem...

Currently displaying 101 – 120 of 162