An estimate from below for the Markov constant of a Cantor repeller

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1. [1] W. Pawłucki and W. Pleśniak, Extension of $C^{\infty }$ functions from sets with polynomial cusps, Studia Math. 88 (1988), 279-287. Zbl0778.26010
2. [2] W. Pawłucki and W. Pleśniak, Prolongement de fonctions $C^{\infty }$, C.R. Acad. Sci. Paris Ser. I 304 (1987), 167-168. 
3. [3] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322-357. Zbl0111.08102
4. [4] L. Białas and A. Volberg, Markov's property of the Cantor ternary set, Studia Math. 104 (1993), 259-268. 
5. [5] P. Jones and Th. Wolff, Hausdorff dimension of harmonic measure in the plane I, Acta Math. 161 (1988), 133-144. 
6. [6] A. Volberg, On the dimension of harmonic measure of Cantor repellers, Michigan Math. J. 40 (1993), 239-258. Zbl0797.30022
7. [7] A. Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Invent. Math. 99 (1990), 627-649. Zbl0820.58038
8. [8] R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lect. Notes in Math. 470 (1975). Zbl0308.28010
9. [9] W. Phillipp and W. Stout, Almost sure invariant principles for partial sums of weakly dependent random variables, Mem. Amer. Math. Soc. 161 (1975). 
10. [10] I. A. Ibragimov and Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff, Groningen, 1971. Zbl0219.60027
11. [11] A. Volberg, On the harmonic measure of self-similar sets on the plane, in: Harmonic Analysis and Discrete Potential Theory, M. Picardello (ed.), Plenum Press, 1991, 267-281.