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Approximation on the sphere by Besov analytic functions

Evgueni Doubtsov — 1997

Studia Mathematica

Boundary values of zero-smooth Besov analytic functions in the unit ball of n are investigated. Bounded Besov functions with prescribed lower semicontinuous modulus are constructed. Correction theorems for continuous Besov functions are proved. An approximation problem on great circles is studied.

Henkin measures, Riesz products and singular sets

Evgueni Doubtsov — 1998

Annales de l'institut Fourier

The mutual singularity problem for measures with restrictions on the spectrum is studied. The d -pluriharmonic Riesz product construction on the complex sphere is introduced. Singular pluriharmonic measures supported by sets of maximal Hausdorff dimension are obtained.

Symmetric and Zygmund measures in several variables

Evgueni DoubtsovArtur 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...

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