The L2‐norm of the Cauchy transform on circular annuli

Wiley

David Kalaj

2026

Abstract We compute the exact operator norm of the Cauchy transform on a circular annulus . Exploiting rotational symmetry and a Fourier mode decomposition, we reduce the problem to a one‐dimensional weighted Hardy operator and obtain where is the first eigenvalue of the Laplacian on with Neumann condition on the inner boundary and Dirichlet condition on the outer boundary. The extremizing modes are explicitly described in terms of Bessel functions.

Wiley

The L2‐norm of the Cauchy transform on circular annuli

Preuzmite dokument 2026 David Kalaj

Cambridge University Press (CUP)

Isoperimetric inequality for nearly spherical domains in the Bergman ball double struck upper B 2$\mathbb{B}_2$ 𝔹 2

We prove a quantitative isoperimetric inequality for nearly spherical domains in the Bergman ball in double struck upper C 2 $\mathbb{C}^2$ ℂ 2...

Preuzmite dokument 2026 David Kalaj

Informa UK Limited

On a Hardy inequality for holomorphic functions

Preuzmite dokument 2025 David Kalaj

Wiley

The radial symmetry of minimizers to the p$p$ weighted Dirichlet energy in R3$\mathbb {R}^3$

AbstractLet and be annuli in . Let , and assume that is the class of Sobolev homeomorphisms of onto . Then, we consider the following Dirichlet‐type energy of : We prove that this energy integral attains its minimum for and , and the minimum is a certain radial diffeomorphism .For general , we minimize the Dirichlet‐type integral throughout the class of radial mappings between given annuli, and this minimum always exists for . For , the image annulus cannot be too thick, which is opposite...

Preuzmite dokument 2024 David Kalaj

European Mathematical Society - EMS - Publishing House GmbH

Erratum to “Harmonic quasiconformal mappings between $\mathcal{C}^1$ smooth Jordan domains”

Preuzmite dokument 2022 David Kalaj