Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Melentijević, Petar"'
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 results are uniform on the parameters of the family of Cauchy wavelets, and
Externí odkaz:
http://arxiv.org/abs/2411.16010
Autor:
Melentijević, Petar
\begin{abstract} Let $P_+$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider the inequalities of the following form $$ \|f\|_{L^p(\mathbb{T})}\leq B_{p,s}\|( |P_ + f | ^s + |P_- f |^s) ^{\frac 1s}\|_{L^p (\mathbb{T})} $$ and prov
Externí odkaz:
http://arxiv.org/abs/2408.02453
Publikováno v:
Math. Ann (2023)
In this paper, we prove that the $L^p(\mathbb{R}^d)$ norm of the maximal truncated Riesz transform in terms of the $L^p(\mathbb{R}^d)$ norm of Riesz transform is dimension-free for any $2\leq p<\infty$, using integration by parts formula for radial F
Externí odkaz:
http://arxiv.org/abs/2306.07406
Autor:
Kalaj, David, Melentijević, Petar
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 of functions from Bergman space with respect to two diferent measures.
Externí odkaz:
http://arxiv.org/abs/2302.13424
Autor:
Melentijević, Petar
\begin{abstract} We obtain sharp $L^p\rightarrow L^q$ hypercontractive inequalities for the weighted Bergman spaces on the unit disk $\mathbb{D}$ with the usual weights \\ $\frac{\alpha-1}{\pi}(1-|z|^2)^{\alpha-2},\alpha>1$ for $q\geq 2,$ thus solvin
Externí odkaz:
http://arxiv.org/abs/2211.03655
Autor:
Melentijević, Petar
Publikováno v:
Math. Ann. (2023)
\begin{abstract} In this paper we address the problem of finding the best constants in inequalities of the form: $$ \|\big(|P_+f|^s+|P_-f|^s\big)^{\frac{1}{s}}\|_{L^p({\mathbb{T}})}\leq A_{p,s} \|f\|_{L^p({\mathbb{T}})},$$ where $P_+f$ and $P_-f$ den
Externí odkaz:
http://arxiv.org/abs/2203.14364
Autor:
Kalaj, David, Melentijevic, Petar
In this paper we solve the longstanding Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. This conjecture states the following. For any minimal graph lying above the entire unit disk, the Gaussian curvature at the point above t
Externí odkaz:
http://arxiv.org/abs/2111.14687
Publikováno v:
Potential Analysis (2022)
\begin{abstract} In this paper, we partly solve the generalized Khavinson conjecture in the setting of hyperbolic harmonic mappings in Hardy space. Assume that $u=\mathcal{P}_{\Omega}[\phi]$ and $\phi\in L^{p}(\partial\Omega, \mathbb{R})$, where $p\i
Externí odkaz:
http://arxiv.org/abs/2009.09548
Let $\mathbb{D}$ be the unit disk and $\varphi\in L^p(\mathbb{D}, \mathrm{d}A)$, where $1\leq p\leq\infty$. For $z\in\mathbb{D}$, the Cauchy-transform on $\mathbb{D}$, denote by $\mathcal{P}$, is defined as follows: $$\mathcal{P}[\varphi](z)=-\int_{\
Externí odkaz:
http://arxiv.org/abs/2008.03068
Autor:
Marković, Marijan, Melentijević, Petar
Publikováno v:
Potential Analysis(2022)
\begin{abstract} Let $P\pm$ be the Riesz's projection operator and let $P_-= I - P_+$. We consider estimates of the expression $\|( |P_ + f | ^s + |P_- f |^s) ^{\frac{1}{s}}\|_{L^p (\mathbf{T})}$ in terms of Lebesgue $p$-norm of the function $f \in L
Externí odkaz:
http://arxiv.org/abs/1912.08944