Oscillation of Functions in the Hölder Class

Autor: Pavel Mozolyako, Artur Nicolau

Publikováno v: Potential Analysis. 55:53-74

We study the size of the set of points where the α-divided difference of a function in the Holder class Λα is bounded below by a fixed positive constant. Our results are obtained from their discrete analogues which can be stated in the language of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3fbc3daf8e2d55a3a89db94cba7ed409
https://doi.org/10.1007/s11118-020-09849-1

Iterates of Blaschke products and Peano curves

Autor: Juan Jesús Donaire, Artur Nicolau

Let $f$ be a finite Blaschke product with $f(0)=0$, which is not a rotation and let $f^{n}$ be its $n$-th iterate. Given a sequence $\{a_{n}\}$ of complex numbers consider $F= \sum a_n f^{n}$. If $\{a_n\}$ tends to $0$ but $\sum |a_n| = \infty $, we

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fc532f690a3d60a7816e49070de4392

Oscillation of Generalized Differences of Hölder and Zygmund Functions

Autor: Alejandro J. Castro, Artur Nicolau, José G. Llorente

Publikováno v: The Journal of Geometric Analysis. 28:1665-1686

In this paper we analyze the oscillation of functions having derivatives in the Holder or Zygmund class in terms of generalized differences and prove that its growth is governed by a version of the classical Kolmogorov’s Law of the Iterated Logarit

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::4d924a9a1a1443bda5667e99ccf401f2
https://doi.org/10.1007/s12220-017-9882-4

Uniform separation, hyperbolic geodesics and zero distribution of solutions of linear differential equations

Autor: Artur Nicolau, Janne Gröhn

Publikováno v: Bulletin of the London Mathematical Society. 49:380-390

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f40069e69216cd7484371871968410d8
https://doi.org/10.1112/blms.12036

The Corona Property in Nevanlinna quotient algebras and Interpolating sequences

Autor: Xavier Massaneda, Pascal J. Thomas, Artur Nicolau

Publikováno v: Journal of Functional Analysis
Journal of Functional Analysis, 2019, 276, pp.2636-2661. ⟨10.1016/j.jfa.2018.08.001⟩
Journal of Functional Analysis, Elsevier, 2019, 276, pp.2636-2661. ⟨10.1016/j.jfa.2018.08.001⟩

Let $I$ be an inner function in the unit disk $\mathbb D$ and let $\mathcal N$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout equations in the quotient algebra $\mathcal N/I\mathcal N$ can be solved if and only if the ze

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c9be70d718093b8977924ee7e894a32
https://hal.science/hal-01766910