1 citations · 1 across the 10 of their papers we have counts for
11 papers
A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded
David Kalaj
We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+\overline g \colon \D\to\C \] such that \[ |g'(z)|\le k|h'(z)|,\qquad z\in\D, \] while the a…
The Norm of the Interior Cauchy Transform: Beyond the First Dirichlet Eigenvalue
David Kalaj
We study sharp \(L^2\) bounds for the interior Cauchy transform \(C_D\) on a bounded planar domain \(D\) and clarify its connection with the Dirichlet spectrum. We analyze an appro…
The -Norm of the Cauchy transform on circular annuli
David Kalaj
We compute the exact operator norm of the Cauchy transform \[ (C_Ωf)(z)=\frac1π\int_Ω\frac{f(w)}{z-w}\,dA(w) \] on a circular annulus . Exploiting rotat…
Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in
Anton Gjokaj, David Kalaj
We prove that every sense-preserving harmonic --quasiconformal homeomorphism between Lyapunov domains (equivalently, bounded domains) in …
Minimal surfaces over the Pitot quadrilaterals
Vladimir Dragović, David Kalaj
We develop a fully explicit framework for constructing Scherk-type minimal graphs over the Pitot quadrilaterals (i.e. such that the two pairs of opposite sides have the same total…
On generalized M. Riesz conjugate function theorem for harmonic mappings
Anton Gjokaj, David Kalaj, Djordjije Vujadinovic
Let be the Lesbegue space of complex-valued functions defined in the unit circle . In this paper, we address the prob…
On a sharp form of curvature conjecture for minimal graphs
David Kalaj
Recently, the author and Melentijević resolved the longstanding Gaussian curvature problem by proving the sharp inequality \[ |\mathcal{K}| < c_0 = \frac{π^2}{2} \] for minimal gra…
Zygmund theorem for harmonic quasiregular mappings
David Kalaj
Let . We prove Zygmund theorem for quasiregular harmonic mappings in the unit disk in the complex plane by providing a constant in the inequality $$…
A sharp estimate of area for sublevel-set of Blaschke products
David Kalaj
Let be the unit disk in the complex plane. Among other results, we prove the following curious result for a finite Blaschke product: $$B(z)=e ^{is}\prod_{k=1}^d \frac{…
Contraction property of Fock type space of log-subharmonic functions in
David Kalaj
We prove a contraction property of Fock type spaces of log-subharmonic functions in . To prove the result, we demonstrate a certain monotonic proper…
On M. Riesz conjugate function theorem for harmonic functions
David Kalaj
Let be the Lesbegue space of complex-valued functions defined in the unit circle . In this paper, we address the prob…