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Smoothness of Green's functions and Markov-type inequalities

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Białas-Cież L.

Banach Center Publications

2011

tom 92

nr 1

27-36

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.

Ograniczanie wyników

1 Banach Center Publications

1 Białas-Cież L.

1 2011

Wyniki wyszukiwania

Smoothness of Green's functions and Markov-type inequalities