Displaying 2021 – 2040 of 2728

Showing per page

Symmetric and Zygmund measures in several variables

Evgueni Doubtsov, Artur Nicolau (2002)

Annales de l’institut Fourier

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

Symmetric products of the Euclidean spaces and the spheres

Naotsugu Chinen (2015)

Commentationes Mathematicae Universitatis Carolinae

By F n ( X ) , n 1 , we denote the n -th symmetric product of a metric space ( X , d ) as the space of the non-empty finite subsets of X with at most n elements endowed with the Hausdorff metric d H . In this paper we shall describe that every isometry from the n -th symmetric product F n ( X ) into itself is induced by some isometry from X into itself, where X is either the Euclidean space or the sphere with the usual metrics. Moreover, we study the n -th symmetric product of the Euclidean space up to bi-Lipschitz equivalence and...

Tchebotaröv’s extremal problem

Promarz Tamrazov (2005)

Open Mathematics

We give the complete solution of the extremal problem posed by N.G. Tchebotaröv in 20th of the last century, and we establish explicit parametric formulae for the extremals.

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 area formula for W 1 , n -mappings

Jan Malý (1994)

Commentationes Mathematicae Universitatis Carolinae

Let f be a mapping in the Sobolev space W 1 , n ( Ω , 𝐑 n ) . Then the change of variables, or area formula holds for f provided removing from counting into the multiplicity function the set where f is not approximately Hölder continuous. This exceptional set has Hausdorff dimension zero.

The Berezin transform and operators on spaces of analytic functions

Karel Stroethoff (1997)

Banach Center Publications

In this article we will illustrate how the Berezin transform (or symbol) can be used to study classes of operators on certain spaces of analytic functions, such as the Hardy space, the Bergman space and the Fock space. The article is organized according to the following outline. 1. Spaces of analytic functions 2. Definition and properties Berezin transform 3. Berezin transform and non-compact operators 4. Commutativity of Toeplitz operators 5. Berezin transform and Hankel or Toeplitz operators 6....

Currently displaying 2021 – 2040 of 2728