No abstract uploaded!

In this paper, we prove a good-λ inequality between the nontangential maximal function and the square area integral of a subharmonic function$u$in a bounded NTA domain$D$in$R$^{$n$}. We achieve this by showing that a weighted Riesz measure of$u$is a Carleson measure, with the Carleson norm bounded by a constant independent of$u$. As consequences of the good-λ inequality, we obtain McConnell-Uchiyama's inequality and an analogue of Murai-Uchiyama's inequality for subharmonic functions in$D$.

No abstract uploaded!

No abstract uploaded!

We prove an analog of Böttcher’s theorem for transcendental entire functions in the Eremenko–Lyubich class $ \mathcal{B} $ . More precisely, let$f$and$g$be entire functions with bounded sets of singular values and suppose that$f$and$g$belong to the same parameter space (i.e., are$quasiconformally equivalent$in the sense of Eremenko and Lyubich). Then$f$and$g$are conjugate when restricted to the set of points that remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane.