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Optimal factors in Vladimir Markov's inequality in L2 norm

Baran M., Kowalska A., Ozorka P.

Science, Technology and Innovation

2018

Vol. 2, no. 1

64--73

In this paper we discuss a problem of computation of constants in Vladimir Markov's type inequality in L2 norm on the interval [-1, 1].

Markov sets in C are not polar

Białas-Cież L.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 1

83-89

We prove that a compact set E of C satysfying the generalized Markov inequality (i.e. for each polynomial P (1) [max {absolute value P'(z) : z belongs to E} is less than or equal M (deg P)^m max{ absolute value P(z) : z belongs to E}], where [M is greater than or equal to 1] and m > 0 are some constants independent of P) is not polar. Moreover cap [(E) is greater than or equal to 1/Mdelta^m(diam E)^1/3] with an absolute constant delta > 0.