The exact value of Jung constants in a class of Orlicz function spaces.

Collectanea Mathematica (2005)

• Volume: 56, Issue: 3, page 253-263
• ISSN: 0010-0757

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Abstract

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Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value:(i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 &lt; CΦ &lt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1;(ii) If FΦ(t) is increasing and CΦ &gt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1])=2-1/CΦ,where CΦ= limt→+∞ tφ(t)/Φ(t).

How to cite

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Yan, Y. Q.. "The exact value of Jung constants in a class of Orlicz function spaces.." Collectanea Mathematica 56.3 (2005): 253-263. <http://eudml.org/doc/41830>.

@article{Yan2005,
abstract = {Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value:(i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 &lt; CΦ &lt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1;(ii) If FΦ(t) is increasing and CΦ &gt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1])=2-1/CΦ,where CΦ= limt→+∞ tφ(t)/Φ(t).},
author = {Yan, Y. Q.},
journal = {Collectanea Mathematica},
keywords = {Espacios de funciones medibles; Espacio de Orlicz},
language = {eng},
number = {3},
pages = {253-263},
title = {The exact value of Jung constants in a class of Orlicz function spaces.},
url = {http://eudml.org/doc/41830},
volume = {56},
year = {2005},
}

TY - JOUR
AU - Yan, Y. Q.
TI - The exact value of Jung constants in a class of Orlicz function spaces.
JO - Collectanea Mathematica
PY - 2005
VL - 56
IS - 3
SP - 253
EP - 263
AB - Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value:(i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 &lt; CΦ &lt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1;(ii) If FΦ(t) is increasing and CΦ &gt; 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1])=2-1/CΦ,where CΦ= limt→+∞ tφ(t)/Φ(t).
LA - eng
KW - Espacios de funciones medibles; Espacio de Orlicz
UR - http://eudml.org/doc/41830
ER -

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