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8 papers · 1 filter
On mappings of finite distortion that are quasiconformal in the unit disk
Olli Hirviniemi, Lauri Hitruhin, István Prause +1
We study quasiconformal mappings of the unit disk that have planar extension with controlled distortion. For these mappings we prove a bound for the modulus of continuity of the in…
On Petrenko's deviations and second order differential equations
J. Heittokangas, M. A. Zemirni
New results on the oscillation of solutions of and on the growth of solutions of are obtained, where and are entire functions. Petrenko's…
Studies of Differences from the point of view of Nevanlinna Theory
Jianhua Zheng, Risto Korhonen
This paper consists of three parts. First, we give so far the best condition under which the shift invariance of the counting function, and of the characteristic of a subharmonic f…
Radial two weight inequality for maximal Bergman projection induced by a regular weight
Taneli Korhonen, José Ángel Peláez, Jouni Rättyä
It is shown in quantitative terms that the maximal Bergman projection \begin{equation*} P^{+}_ω(f)(z)=\int_\mathbb{D} f(ζ)|B^ω_z(ζ)|ω(ζ)\,dA(ζ), \end{equation*} is bounded from $L^…
Criteria for bounded valence of harmonic mappings
Juha-Matti Huusko, María J. Martín
In 1984, Gehring and Pommerenke proved that if the Schwarzian derivative of a locally univalent analytic function in the unit disk satisfies that $\limsup_{|z|\to 1} |S(…
Embedding theorems for Bergman spaces via harmonic analysis
José Ángel Peláez, Jouni Rättyä
Let denote the Bergman space in the unit disc induced by a radial weight~ with the doubling property . The positiv…