# Markov inequality on sets with polynomial parametrization

Annales Polonici Mathematici (1994)

- Volume: 60, Issue: 1, page 69-79
- ISSN: 0066-2216

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topMirosław Baran. "Markov inequality on sets with polynomial parametrization." Annales Polonici Mathematici 60.1 (1994): 69-79. <http://eudml.org/doc/262450>.

@article{MirosławBaran1994,

abstract = {The main result of this paper is the following: if a compact subset E of $ℝ^n$ is UPC in the direction of a vector $v ∈ S^\{n-1\}$ then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].},

author = {Mirosław Baran},

journal = {Annales Polonici Mathematici},

keywords = {extremal function; Markov inequality; UPC sets; uniformly polynomially cuspidal},

language = {eng},

number = {1},

pages = {69-79},

title = {Markov inequality on sets with polynomial parametrization},

url = {http://eudml.org/doc/262450},

volume = {60},

year = {1994},

}

TY - JOUR

AU - Mirosław Baran

TI - Markov inequality on sets with polynomial parametrization

JO - Annales Polonici Mathematici

PY - 1994

VL - 60

IS - 1

SP - 69

EP - 79

AB - The main result of this paper is the following: if a compact subset E of $ℝ^n$ is UPC in the direction of a vector $v ∈ S^{n-1}$ then E has the Markov property in the direction of v. We present a method which permits us to generalize as well as to improve an earlier result of Pawłucki and Pleśniak [PP1].

LA - eng

KW - extremal function; Markov inequality; UPC sets; uniformly polynomially cuspidal

UR - http://eudml.org/doc/262450

ER -

## References

top- [B1] M. Baran, Bernstein type theorems for compact sets in ${\mathbb{R}}^{n}$, J. Approx. Theory 69 (1992), 156-166. Zbl0748.41008
- [B2] M. Baran, Complex equilibrium measure and Bernstein type theorems for compact sets in ${\mathbb{R}}^{n}$, Proc. Amer. Math. Soc., to appear.
- [B3] M. Baran, Plurisubharmonic extremal function and complex foliation for a complement of a convex subset of ${\mathbb{R}}^{n}$, Michigan Math. J. 39 (1992), 395-404.
- [B4] M. Baran, Bernstein type theorems for compact sets in ${\mathbb{R}}^{n}$ revisited, J. Approx. Theory, to appear.
- [C] E. W. Cheney, Introduction to Approximation Theory, New York, 1966. Zbl0161.25202
- [G] P. Goetgheluck, Inégalité de Markov dans les ensembles effilés, J. Approx. Theory 30 (1980), 149-154. Zbl0457.41015
- [PP1] W. Pawłucki and W. Pleśniak, Markov’s inequality and ${C}^{\infty}$ functions with polynomial cusps, Math. Ann. 275 (1986), 467-480. Zbl0579.32020
- [PP2] W. Pawłucki and W. Pleśniak, Extension of ${C}^{\infty}$ functions from sets with polynomial cusps, Studia Math. 88 (1989), 279-287. Zbl0778.26010
- [P] W. Pleśniak, Markov’s inequality and the existence of an extension operator for ${C}^{\infty}$ functions, J. Approx. Theory 61 (1990), 106-117. Zbl0702.41023
- [S] J. Siciak, Extremal plurisubharmonic functions in ${\u2102}^{n}$, Ann. Polon. Math. 39 (1981), 175-211. Zbl0477.32018
- [Z] M. Zerner, Développement en série de polynômes orthonormaux des fonctions indéfiniment différentiables, C. R. Acad. Sci. Paris 268 (1969), 218-220. Zbl0189.14601

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