D. Kalaj

activity

20072026

most citedLipschitz spaces and harmonic mappings

24 citations · 152 across the 76 of their papers we have counts for

collaborators

Showing 2010 · math.CVShow all

8 papers · 2 filters

math.CV2010★ 2 cited

Optimal estimates for the gradient of harmonic functions in the unit disk

David Kalaj, Marijan Markovic

Concrete sharp constants in a pointwise estimate of the gradient of a harmonic function in the unit disk are obtained under the assumption that function belong to Hardy space $h^{p}$ …

math.CV2010

Harmonic mappings and distance function

David Kalaj

We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with $C^{1, α}$ ( $α < 1$ ), respectively $C^{1, 1}$ compact boundary is bi-Lipschitz. The…

math.CV2010★ 1 cited

Radial extension of a bi-Lipschitz parametrization of a starlike Jordan curve

David Kalaj

In this paper we discus the radial extension $w$ of a bi-Lipschitz parameterization $F (e^{i t}) = f (t)$ of a starlike Jordan curve $γ$ w.r. to 0. We show that, if parameterization is…

math.CV2010

On harmonic functions and the Schwarz lemma

David Kalaj, Matti Vuorinen

We study the Schwarz lemma for harmonic functions and prove sharp versions for the cases of real harmonic functions and the norm of harmonic mappings.

math.CV2010★ 20 cited

Deformations of Annuli on Riemann surfaces with Smallest Mean Distortion

David Kalaj

Let $A$ and $A^{'}$ be two circular annuli and let $ρ$ be a radial metric defined in the annulus $A^{'}$ . Consider the class $H_{ρ}$ of $ρ -$ harmonic mappings between $A$ and $A^{'}$ .…

math.CV2010

Cauchy transform and Poisson's equation

David Kalaj

Let $u \in W_{0}^{2, p}$ , $1 \leq p \leq \infty$ be a solution of the Poisson equation $Δ u = h$ , $h \in L^{p}$ , in the unit disk. It is proved that $∥\nabla u ∥_{L^{p}} \leq a_{p} ∥ h ∥_{L^{p}}$ wit…