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Squeezing the Sierpinski sponge

Tadeusz Iwaniec, Gaven Martin (2002)

Studia Mathematica

We give an example relating to the regularity properties of mappings with finite distortion. This example suggests conditions to be imposed on the distortion function in order to avoid "cavitation in measure".

Stability of the bases and frames reproducing kernels in model spaces

Anton Baranov (2005)

Annales de l'institut Fourier

We study the bases and frames of reproducing kernels in the model subspaces K Θ 2 = H 2 Θ H 2 of the Hardy class H 2 in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels k λ n ( z ) = ( 1 - Θ ( λ n ) ¯ Θ ( z ) ) / ( z - λ ¯ n ) under “small” perturbations of the points λ n . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces K Θ 2 and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

Starlike functions of complex order involving q-hypergeometric functions with fixed point

Kaliappan Vijaya, Gangadharan Murugusundaramoorthy, Murugesan Kasthuri (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Recently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities...

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