Smoothness of Green's functions and Markov-type inequalities

• Autorzy: Leokadia Białas-Cież
• Języki publikacji: EN

Abstrakty

EN

Let E be a compact set in the complex plane, $g_{E}$ be the Green function of the unbounded component of $ℂ_{∞}∖E$ with pole at infinity and $Mₙ(E) = sup (||P'||_{E})/(||P||_{E})$ where the {supremum} is taken over all polynomials $P|_{E} ≢ 0$ of degree at most n, and $||f||_{E} = sup{|f(z)| : z ∈ E}$. The paper deals with recent results concerning a connection between the smoothness of $g_{E}$ (existence, continuity, Hölder or Lipschitz continuity) and the growth of the sequence ${Mₙ(E)}_{n = 1,2,...}$. Some additional conditions are given for special classes of sets.

Kategorie tematyczne

• 30-02: Research exposition (monographs, survey articles)
• 31-02: Research exposition (monographs, survey articles)
• 30A10: Inequalities in the complex domain
• 31C15: Potentials and capacities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 92
• Numer: 1
• Strony: 27-36

Daty

wydano

2011

Twórcy

autor

Leokadia Białas-Cież

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/bc92-0-2