Uniform approximation of functions in Jordan domains

Polynomial approximation of analytic functions on a finite number of continua in the complex plane

“…There is a number of definitions of these moduli in the complex plane (see [16]). The definition by Dyn'kin [7] is the simplest to explain. Set k ∈ N, and let z 1 , . .…”

Constructive description of Hölder-like classes on an arc in R3 by means of harmonic functions

“…We observe that definitions (20) and (21) imply the estimate gradd 2 (M) ≤ C. Finally, we put (22) gives the required function d 0 . We have the following estimates:…”

“…The main problem in that direction was to weaken the assumptions concerning the boundary Γ. The results 20 progressed from a piecewise smooth in some sense [7,8,9] to a chord-arc [10] and finally to a quasiconformal property of a Jordan curve Γ [11].…”

Estimates of analytic functions in Jordan domain

“…The results of the paper constitute the technical foundation for the study of spaces of analytic functions in Jordan domains (cf., e.g., [6][7][8] If F is a rectifiable curve in C , and I, ~cF, is an arc, then III is the length of the arc ~ ; v _~r~ is the integral of the function f with respect to arc length. ~ ~, if 0 < ci < Ifl/Igl < c2 < =.…”