Smoothness of Green's functions and Markov-type inequalities

Leokadia Białas-Cież

Banach Center Publications, Tome 95 (2011), p. 27-36 / Harvested from The Polish Digital Mathematics Library

Résumé

Let E be a compact set in the complex plane, $g_{E}$ be the Green function of the unbounded component of $ℂ_{\infty} ∖ E$ with pole at infinity and $M ₙ (E) = s u p (| | P^{'} {| |}_{E} {) / (| | P | |}_{E})$ where the supremum is taken over all polynomials ${P |}_{E} ≢ 0$ of degree at most n, and ${| | f | |}_{E} = s u p | f (z) | : z \in E$ . 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 ${M ₙ (E)}_{n = 1, 2, . . .}$ . Some additional conditions are given for special classes of sets.

Publié le : 2011-01-01

Zbl 1229.31001

EUDML-ID : urn:eudml:doc:281729

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-2,
     author = {Leokadia Bia\l as-Cie\.z},
     title = {Smoothness of Green's functions and Markov-type inequalities},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {27-36},
     zbl = {1229.31001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-2}
}

Leokadia Białas-Cież. Smoothness of Green's functions and Markov-type inequalities. Banach Center Publications, Tome 95 (2011) pp. 27-36. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-2/