Markov's property of the Cantor ternary set

Leokadia Białas; Alexander Volberg

Studia Mathematica (1993)

  • Volume: 104, Issue: 3, page 259-268
  • ISSN: 0039-3223

Abstract

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We prove that the Cantor ternary set E satisfies the classical Markov inequality (see [Ma]): for each polynomial p of degree at most n (n = 0, 1, 2,...) (M) | p ' ( x ) | ≤ M n m s u p E | p | for x ∈ E, where M and m are positive constants depending only on E.

How to cite

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Białas, Leokadia, and Volberg, Alexander. "Markov's property of the Cantor ternary set." Studia Mathematica 104.3 (1993): 259-268. <http://eudml.org/doc/215974>.

@article{Białas1993,
abstract = {We prove that the Cantor ternary set E satisfies the classical Markov inequality (see [Ma]): for each polynomial p of degree at most n (n = 0, 1, 2,...) (M) $|p^\{\prime \}(x)| ≤ Mn^\{m\} sup_\{E\}|p|$ for x ∈ E, where M and m are positive constants depending only on E.},
author = {Białas, Leokadia, Volberg, Alexander},
journal = {Studia Mathematica},
keywords = {Markov inequality},
language = {eng},
number = {3},
pages = {259-268},
title = {Markov's property of the Cantor ternary set},
url = {http://eudml.org/doc/215974},
volume = {104},
year = {1993},
}

TY - JOUR
AU - Białas, Leokadia
AU - Volberg, Alexander
TI - Markov's property of the Cantor ternary set
JO - Studia Mathematica
PY - 1993
VL - 104
IS - 3
SP - 259
EP - 268
AB - We prove that the Cantor ternary set E satisfies the classical Markov inequality (see [Ma]): for each polynomial p of degree at most n (n = 0, 1, 2,...) (M) $|p^{\prime }(x)| ≤ Mn^{m} sup_{E}|p|$ for x ∈ E, where M and m are positive constants depending only on E.
LA - eng
KW - Markov inequality
UR - http://eudml.org/doc/215974
ER -

References

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  14. [R-S] Q. I. Rahman and G. Schmeisser, Les inégalités de Markoff et de Bernstein, Les Presses de l'Université de Montréal, 1983. 
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