Petar Melentijević

activity

20192026

most citedHypercontractive inequalities for weighted Bergman spaces

6 citations · 6 across the 3 of their papers we have counts for

collaborators

7 papers

math.CV2026

Reverse Heinz type inequality, Mather beta function and coefficient estimates

Vladimir Božin, Petar Melentijević

In this paper, we prove that for two cyclically ordered sequences of complex numbers of unit modulus $(ξ_{j})_{j = 1}^{n}$ and $(ζ_{j})_{j = 1}^{n}$ the inequality: $$\bigg|\sum_{m=1}^{n}(…

math.CV2022★ 6 cited

Hypercontractive inequalities for weighted Bergman spaces

Petar Melentijević

\begin{abstract} We obtain sharp $L^{p} \to L^{q}$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $D$ with the usual weights \\ $\frac{α…

math.DG2021

Gaussian curvature conjecture for minimal graphs

David Kalaj, Petar Melentijevic

In this paper, we solve the longstanding Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. The conjecture asserts that for any minimal graph above the unit d…

math.AP2020

Khavinson problem for hyperbolic harmonic mappings in Hardy space

Jiaolong Chen, David Kalaj, Petar Melentijević

\begin{abstract} In this paper, we partly solve the generalized Khavinson conjecture in the setting of hyperbolic harmonic mappings in Hardy space. Assume that $u = P_{Ω} [ϕ]$ …

math.CV2020

$L^{p}$ -theory for Cauchy-transform on the unit disk

David Kalaj, Petar Melentijević, Jian-Feng Zhu

Let $D$ be the unit disk and $φ \in L^{p} (D, d A)$ , where $1 \leq p \leq \infty$ . For $z \in D$ , the Cauchy-transform on $D$ , denote by $\mathca…

math.FA2019

Best constants in inequalities involving analytic and co-analytic projections and Riesz theorem for various function spaces

Marijan Marković, Petar Melentijević

\begin{abstract} Let $P \pm$ be the Riesz's projection operator and let $P_{-} = I - P_{+}$ . We consider estimates of the expression $\|( |P_ + f | ^s + |P_- f |^s) ^{\frac{1}{s}}\|_{L^p…