arXiv subjects

Miodrag Mateljevic

Publications and source records attributed to Miodrag Mateljevic.

4 recordsLinked to original sources

arXiv2026

On Montel theorem for mappings with inverse moduli inequalities

This paper is devoted to the study of mappings with finite distortion, in particular, mappings satisfying the inverse Poletskii inequality. We study the problem of equicontinuity of families of such mappings in a given domain. We establish that a family of open discrete mappings with the inverse Poletskii inequality, omitting at least one point, is equicontinuous if the majorant responsible for the distortion of the modulus of families of paths under the mapping is integrable over almost all concentric spheres centered at the given point. Since analytic functions with finite multiplicity satisfy the inverse Poletskii inequality, this result generalizes the well-known Montel theorem on the normality of families.

math.CV↗

arXiv2023

$H^p$ theory of separately $(α, β)$-harmonic functions in the unit polydisc

We prove existence and uniqueness of a solution of the Dirichlet problem for separately $(α, β)$ - harmonic functions on the unit polydisc $\mathbb D^n$ with boundary data in $C(\mathbb T^n)$ using $(α, β)$ - Poisson kernel. A characterization by hypergeometric functions of such functions which are also m - homogeneous is given, this characterization is used to obtain series expansion of these functions. Basic $H^p$ theory of such functions is developed: integral representations by measures and $L^p$ functions on $\mathbb T^n$, norm and weak star convergence at the distinguished boundary $\mathbb T^n$. Weak $(1, 1)$ - type estimate for a restricted non-tangential maximal function is derived. Slice functions $u(z_1, . . . , z_k, ζ_{k+1}, . . . , ζ_n)$, where some of the variables are fixed, are shown to belong in the appropriate space of functions of $k$ variables. We prove a Fatou type theorem on a. e. existence of restricted non-tangential limits for these functions and a corresponding result for unrestricted limit at a point in $\mathbb T^n$. Our results extend earlier results for $(α, β)$ harmonic functions in the disc and for n - harmonic functions in $\mathbb D^n$.

math.CV↗

arXiv2012

Charatheodory and Smirnov type theorem for harmonic mappings

We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions of the boundary.

math.CV↗

arXiv2010

On certain nonlinear elliptic PDE and quasiconfomal mapps between Euclidean surfaces

We mainly investigate some properties of quasiconformal mappings between smooth 2-dimensional surfaces with boundary in the Euclidean space, satisfying certain partial differential equations (inequalities) concerning Laplacian, and in particular satisfying Laplace equation and show that that these mappings are Lipschitz. Conformal parametrization of such surfaces and the method developed in our paper \cite{km} have important role in this paper.dan curves and is extended to the case of $C^{2,α}$ surfaces with smooth and compact boundary.

math.CV↗