# Smoothness of Green's functions and Markov-type inequalities

Banach Center Publications (2011)

- Volume: 92, Issue: 1, page 27-36
- ISSN: 0137-6934

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topLeokadia Białas-Cież. "Smoothness of Green's functions and Markov-type inequalities." Banach Center Publications 92.1 (2011): 27-36. <http://eudml.org/doc/281729>.

@article{LeokadiaBiałas2011,

abstract = {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 $Mₙ(E) = sup (||P^\{\prime \}||_\{E\})/(||P||_\{E\})$ 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.},

author = {Leokadia Białas-Cież},

journal = {Banach Center Publications},

keywords = {Green function; polynomial; Markov inequality; polar set; Cantor set},

language = {eng},

number = {1},

pages = {27-36},

title = {Smoothness of Green's functions and Markov-type inequalities},

url = {http://eudml.org/doc/281729},

volume = {92},

year = {2011},

}

TY - JOUR

AU - Leokadia Białas-Cież

TI - Smoothness of Green's functions and Markov-type inequalities

JO - Banach Center Publications

PY - 2011

VL - 92

IS - 1

SP - 27

EP - 36

AB - 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 $Mₙ(E) = sup (||P^{\prime }||_{E})/(||P||_{E})$ 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.

LA - eng

KW - Green function; polynomial; Markov inequality; polar set; Cantor set

UR - http://eudml.org/doc/281729

ER -

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