24 citations · 152 across the 76 of their papers we have counts for
10 papers · 1 filter
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 …
Harmonic mappings and distance function
David Kalaj
We prove the following theorem: every quasiconformal harmonic mapping between two plane domains with (), respectively compact boundary is bi-Lipschitz. The…
Radial extension of a bi-Lipschitz parametrization of a starlike Jordan curve
David Kalaj
In this paper we discus the radial extension of a bi-Lipschitz parameterization of a starlike Jordan curve w.r. to 0. We show that, if parameterization is…
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.
On quasiconformal selfmappings of the unit disk and elliptic PDE in the plane
David Kalaj
We prove the following theorem: if is a quasiconformal mapping of the unit disk onto itself satisfying elliptic partial differential inequality $|L[w]|\le \mathcal{B}|\nabla w|…
Norm inequalities for vector functions
Barkat A. Bhayo, Vladimir Božin, David Kalaj +1
We study vector functions of into itself, which are of the form where is a continuous function and call thes…