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The angular distribution of mass by Bergman functions.

Donald E. Marshall, Wayne Smith (1999)

Revista Matemática Iberoamericana

Let D = {z: |z| < 1} be the unit disk in the complex plane and denote by dA two-dimensional Lebesgue measure on D. For ε > 0 we define Σε = {z: |arg z| < ε}. We prove that for every ε > 0 there exists a δ > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 thenThis problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.

The Bergman projection on weighted spaces: L¹ and Herz spaces

Oscar Blasco, Salvador Pérez-Esteva (2002)

Studia Mathematica

We find necessary and sufficient conditions on radial weights w on the unit disc so that the Bergman type projections of Forelli-Rudin are bounded on L¹(w) and in the Herz spaces K p q ( w ) .

The Bloch space for the minimal ball

G. Mengotti (2001)

Studia Mathematica

We introduce the Bloch space for the minimal ball and we prove that this space can be identified with the dual of a certain analytic space which is strongly related to the Bergman theory on the minimal ball.

The C k Space

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].

The Campanato, Morrey and Hölder spaces on spaces of homogeneous type

Eiichi Nakai (2006)

Studia Mathematica

We investigate the relations between the Campanato, Morrey and Hölder spaces on spaces of homogeneous type and extend the results of Campanato, Mayers, and Macías and Segovia. The results are new even for the ℝⁿ case. Let (X,d,μ) be a space of homogeneous type and (X,δ,μ) its normalized space in the sense of Macías and Segovia. We also study the relations of these function spaces for (X,d,μ) and for (X,δ,μ). Using these relations, we can show that theorems for the Campanato, Morrey or Hölder spaces...

The functor σ²X

Stevo Todorčević (1995)

Studia Mathematica

We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.

The level function in rearrangement invariant spaces.

Gord Sinnamon (2001)

Publicacions Matemàtiques

An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.

The Lindelöf property and σ-fragmentability

B. Cascales, I. Namioka (2003)

Fundamenta Mathematicae

In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space [ - 1 , 1 ] D is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of [ - 1 , 1 ] D is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then...

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