Markov's property of the Cantor ternary set

 Access to full text

 Full (PDF)

1. [Fe] M. Fekete, Über die Verteilung der Wurzeln bei gewissen algebraischen Gleichungen mit ganzzahligen Koeffizienten, Math. Z. 17 (1923), 228-249. 
2. [H-K] W. K. Hayman and P. B. Kennedy, Subharmonic Functions, Vol. I, Academic Press, 1976. Zbl0419.31001
3. [La] N. S. Landkof, Foundations of Modern Potential Theory, Springer, 1972. Zbl0253.31001
4. [Lj1] F. Leja, Sur les suites de polynômes, les ensembles fermés et la fonction de Green, Ann. Soc. Polon. Math. 12 (1933), 57-71. Zbl61.0356.08
5. [Lj2] F. Leja, Theory of Analytic Functions, PWN, Warszawa 1957 (in Polish). 
6. [M-V] N. Makarov and A. Volberg, On the harmonic measure of discontinuous fractals, LOMI preprint E-6-86, Leningrad 1986. 
7. [Ma] A. A. Markov, On a problem posed by D. I. Mendeleev, Izv. Akad. Nauk St-Petersbourg 62 (1889), 1-24 (in Russian). 
8. [Pa-Pl 1] W. Pawłucki and W. Pleśniak, Markov’s inequality and $C^{\infty }$ functions on sets with polynomial cusps, Math. Ann. 275 (3) (1986), 467-480. Zbl0579.32020
9. [Pa-Pl 2] W. Pawłucki and W. Pleśniak, Extension of $C^{\infty }$ functions from sets with polynomial cusps, Studia Math. 88 (1988), 279-287. Zbl0778.26010
10. [Pl 1] W. Pleśniak, Quasianalytic functions in the sense of Bernstein, Dissertationes Math. 147 (1977). 
11. [Pl 2] W. Pleśniak, A Cantor regular set which does not have Markov's property, Ann. Polon. Math. 51 (1990), 269-274. Zbl0739.30008
12. [Pl 3] W. Pleśniak, Compact subsets of ${ℂ}^n$ preserving Markov’s inequality, Mat. Vesnik 40 (1988), 295-300. Zbl0702.32007
13. [Pl 4] W. Pleśniak, Markov’s inequality and the existence of an extension operator for $C^{\infty }$ functions, J. Approx. Theory 61 (1990), 106-117. 
14. [R-S] Q. I. Rahman and G. Schmeisser, Les inégalités de Markoff et de Bernstein, Les Presses de l'Université de Montréal, 1983. 
15. [Si 1] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (2) (1962), 322-357. Zbl0111.08102
16. [Si 2] J. Siciak, Degree of convergence of some sequences in the conformal mapping theory, Colloq. Math. 16 (1967), 49-59. 
17. [Si 3] J. Siciak, An example of a Cantor set preserving Markov's inequality, manuscript, Jagiellonian University, Kraków 1987. 
18. [Ts] M. Tsuji, Potential Theory in Modern Function Theory, Maruzen, Tokyo 1959. Zbl0087.28401

1. Józef Siciak, Wiener's type regularity criteria on the complex plane
2. Alexander Volberg, An estimate from below for the Markov constant of a Cantor repeller