Zobrazeno 1 - 10
of 90
pro vyhledávání: '"KHALFALLAH, ADEL"'
We study Lipschitz continuity for solutions of the $\bar{\alpha}$-Poisson equation in planar cases. We also review some recently obtained results. As corolary we can restate results for harmonic and gradient harmonic functions.
Externí odkaz:
http://arxiv.org/abs/2308.10116
Autor:
Khalfallah, Adel, Mhamdi, Mohamed
Suppose $\alpha,\beta \in \mathbb{R}\backslash \mathbb{Z}^-$ such that $\alpha+\beta>-1$ and $1\leq p \leq \infty$. Let $u=P_{\alpha,\beta}[f]$ be an $(\alpha,\beta)$-harmonic mapping on $\mathbb{D}$, the unit disc of $\mathbb{C}$, with the boundary
Externí odkaz:
http://arxiv.org/abs/2304.12838
Autor:
Khalfallah, Adel, Mateljević, Miodrag
Let $f = P[F]$ denote the Poisson integral of $F$ in the unit disk $\mathbb{D}$ with $F$ is an absolute continuous in the unit circle $\mathbb{T}$ and $\dot{F}\in L^p(\mathbb{T})$, where $\dot{F}(e^{it}) = \frac{d}{dt} F(e^{it})$ and $p \in [1,\infty
Externí odkaz:
http://arxiv.org/abs/2302.09623
Autor:
Khalfallah, Adel, Mateljević, Miodrag
Suppose $\alpha>-1$ and $1\leq p \leq \infty$. Let $f=P_{\alpha}[F]$ be an $\alpha$-harmonic mapping on $\mathbb{D}$ with the boundary $F$ being absolute continuous and $\dot{F}\in L^p(0,2\pi)$, where $\dot{F}(e^{i\theta}):=\frac{dF(e^{i\theta})}{d\t
Externí odkaz:
http://arxiv.org/abs/2302.09613
Let $\mathcal{A}$ be an alphabet of size $n\ge 2$. In this paper, we give a complete description of primitive words $p\neq q$ over an alphabet $\mathcal{A}$ of size $n\geq2$ such that $pq$ is non-primitive and $|p|=2|q|$. In particular, if $l$ is s a
Externí odkaz:
http://arxiv.org/abs/2202.09091
We establish some inequalities of Schwarz-Pick type for harmonic and hyperbolic harmonic functions on the unit ball of and we disprove a recent conjecture of Liu [Schwarz-Pick Lemma for Harmonic Functions, International Mathematics Research Notices,
Externí odkaz:
http://arxiv.org/abs/2111.02618
In this paper, we prove the Khavinson conjecture for hyperbolic harmonic functions on the unit ball. This conjecture was partially solved in \cite{JKM2020}.
Externí odkaz:
http://arxiv.org/abs/2103.00638
In this paper, we establish some Schwarz type lemmas for mappings $\Phi$ satisfying the inhomogeneous biharmonic Dirichlet problem $ \Delta (\Delta(\Phi)) = g$ in $\mathbb{D}$, $\Phi=f$ on $\mathbb{T}$ and $\partial_n \Phi=h$ on $\mathbb{T}$, where $
Externí odkaz:
http://arxiv.org/abs/2003.11460
Autor:
Mateljević, Miodrag, Khalfallah, Adel
We establish some Schwarz type Lemmas for mappings defined on the unit disk with bounded Laplacian. Then we apply these results to obtain boundary versions of the Schwarz lemma.
Externí odkaz:
http://arxiv.org/abs/1810.08823
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 September 2022 513(2)
