arXiv subjects

Vladan Jaguzović

Publications and source records attributed to Vladan Jaguzović.

3 recordsLinked to original sources

arXiv2026

Stability of Wehrl-type Functionals and Concentration Estimates on Bergman Spaces of Log-Subharmonic Functions on the Unit Sphere

In this paper, we consider weighted Bergman classes $\mathcal{B}_{α,p}$ of real-analytic functions on $\mathbb{R}^{n}$, $n\geq 2$ whose moduli are log-subharmonic with respect to the spherical metric. Using the isoperimetric inequality for the spherical metric we prove a certain monotonicity property for super-level sets of $|f(x)|^p\mathcal{W}_n^α(x),$ where $f\in \mathcal{B}_{α,p}$ and $\mathcal{W}_n^α(x)$ is the Bergman weight. As a consequence, we obtain sharp concentration estimates and solve maximization problems for convex Wehrl-type functionals. We also establish quantitative stability estimates, including a bound for the distance of $|f|$ from spherical comparison profiles in terms of the concentration deficit.

math.CV↗

arXiv2026

Toeplitz operators on pluriharmonic Fock spaces

In this paper, we study Toeplitz operators with a positive symbol on pluriharmonic Fock spaces over $\mathbb{C}^{n}.$ We characterize the conditions under which the Toeplitz operator $T_μ$ is bounded, compact, or belongs to the Schatten class $S_1$. Furthermore, we give a necessary condition for a Toeplitz operator to belong to $S_p$ for $p \geq 1,$ and under an additional assumption, we prove the sufficiency of the condition.

math.CV↗

arXiv2025

On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$ and reverse Riesz-type inequalities for $2<p<4$

Let $P_+$ be the Riesz's projection operator and let $P_-=I-P_+.$ We find the best upper estimates of the expression $\left\lVert \left( \left\lvert P_+f \right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} \right\rVert _p $ in terms of Lebesgue p-norm of the function $f \in L^p(\mathbf{T})$ for $p \in (4/3,2)$ and $0 < s \leq \frac{p}{p-1},$ thus extending results from \cite{Melentijevic_2022} and \cite{Melentijevic_2023}, where the mentioned range is not considered. Also, we find the best lower estimates of the same quantities for $p \in (2,4)$ and $s \geq \frac{p}{p-1},$ thus extending results from \cite{melentijevic-reverse-2025}.

math.CV↗