4 papers · 1 filter
Norm inequalities for weighted Dirichlet spaces with applications to conformal maps
Fernando Pérez-González, Jouni Rättyä, Toni Vesikko
A variety of norm inequalities related to Bergman and Dirichlet spaces induced by radial weights are considered. Some of the results obtained can be considered as generalizations o…
Integral means of derivatives of univalent functions in Hardy spaces
Fernando Pérez-González, Jouni Rättyä, Toni Vesikko
We show that the norm in the Hardy space satisfies \begin{equation}\label{absteq} \|f\|_{H^p}^p\asymp\int_0^1M_q^p(r,f')(1-r)^{p\left(1-\frac1q\right)}\,dr+|f(0)|^p\tag† \end…
Growth estimates for meromorphic solutions of higher order algebraic differential equations
Shamil Makhmutov, Jouni Rättyä, Toni Vesikko
We establish pointwise growth estimates for the spherical derivative of solutions of the first order algebraic differential equations. A generalization of this result to higher ord…
On Becker's univalence criterion
Juha-Matti Huusko, Toni Vesikko
We study locally univalent functions analytic in the unit disc of the complex plane such that holds for all $z\in\mathbb{…