19 citations · 36 across the 8 of their papers we have counts for
8 papers
Sharp stability of convex functionals on weighted Bergman spaces with applications
Petar Melentijević
Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We show a sharp quantitative stability of t…
Uniform stability of concentration inequalities and applications
Jaime Gómez, David Kalaj, Petar Melentijević +1
We prove a sharp quantitative version of recent Faber-Krahn inequalities for the continuous Wavelet transforms associated to a certain family of Cauchy wavelet windows . Our result…
Best constants in reverse Riesz-type inequalities for analytic and co-analytic projections
Petar Melentijević
Let be the Riesz's projection operator and let . We consider the inequalities of the following form $$ \|f\|_{L^p(\mathbb{T})}\leq B_{p,s}\|( |P_ + f | ^s + |P_…
Weighted contractivity for derivatives of functions in the Bergman space on the unit disk
David Kalaj, Petar Melentijević
In a recent paper, Ramos and Tilli proved certain sharp inequality for analytic functions in subdomains of the unit disk. We will generalize their main inequality for derivatives o…
Hollenbeck-Verbitsky conjecture on best constant inequalities for analytic and co-analytic projections
Petar Melentijević
\begin{abstract} In this paper we address the problem of finding the best constants in inequalities of the form: $$ \|\big(|P_+f|^s+|P_-f|^s\big)^{\frac{1}{s}}\|_{L^p({\mathbb{T}})…
A proof of the Khavinson conjecture
Petar Melentijević
\begin{abstract} This paper deals with an extremal problem for bounded harmonic functions in the unit ball We solve the Khavinson conjecture in an i…
Norm of the Bergman projection onto the Bloch space with invariant gradient
Petar Melentijević
The value of the operator norm of Bergman projections from to Bloch space is found in \cite{KalajMarkovic2014}. The authors of mentioned paper proposed t…
On the norm of the weighted Berezin transform
Petar Melentijević
We consider a weighted Berezin transform: defined, for and $z \in…