An estimate for the Green’s function

Research output: Contribution to journalArticlepeer-review


Let K be a continuum on ℂ and let gΩ(K)(z,∞) be the Green’s function of Ω(K) = ℂ¯\K. In a recent paper, V. Totik proved that gΩ(K)(z0,∞) ≤ C dist(z0,∞)1/2 with some non-sharp constant C depending only on the diameter of K. He also used this inequality to prove new results on polynomial approximation in C. In this note we prove a sharp version of Totik’s inequality and discuss a conjectural sharp lower bound for gΩ(K)(z0,∞).

Original languageEnglish
Pages (from-to)3067-3074
Number of pages8
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 1 2014


  • Extremal problem
  • Green’s function


Dive into the research topics of 'An estimate for the Green’s function'. Together they form a unique fingerprint.

Cite this