David Kalaj

activity

20232026

most citedA sharp estimate of area for sublevel-set of Blaschke products

1 citations · 1 across the 10 of their papers we have counts for

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4 papers · 1 filter

math.CV2026

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…

math.CV2026

The $L^{2}$ 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…

math.CV2026

The $L^{2}$ -Norm of the Cauchy transform on circular annuli

David Kalaj

We compute the exact $L^{2}$ operator norm of the Cauchy transform \[ (C_Ωf)(z)=\frac1π\int_Ω\frac{f(w)}{z-w}\,dA(w) \] on a circular annulus $Ω = A (r, R) = {r < ∣ z ∣ < R}$ . Exploiting rotat…

math.AP2026

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in $R^{n}$

Anton Gjokaj, David Kalaj

We prove that every sense-preserving harmonic $K$ --quasiconformal homeomorphism $f : D \to Ω$ between Lyapunov domains (equivalently, bounded $C^{1, α}$ domains) in $R^{n}$ …

A bounded globally univalent quasiconformal harmonic map whose analytic part is unbounded

The L2 Norm of the Interior Cauchy Transform: Beyond the First Dirichlet Eigenvalue

The L2-Norm of the Cauchy transform on circular annuli

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in Rn

The $L^{2}$ Norm of the Interior Cauchy Transform: Beyond the First Dirichlet Eigenvalue

The $L^{2}$ -Norm of the Cauchy transform on circular annuli

Lipschitz regularity of harmonic quasiconformal maps between Lyapunov domains in $R^{n}$