On the exact value of Jung constants of Orlicz sequence spaces

• Autores: Y. Q. Yan
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 55, Fasc. 2, 2004, págs. 163-170
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The main result of this paper is: $JC(\ell^{(\Phi)}) = JC(\ell^\Phi) = 2^{1/C^0_\Phi-1}$ under some condition, where $JC(\ell^{(\Phi)})$, $JC(\ell^\Phi)$ are Jung constants of Orlicz sequence space $\ell^\Phi$ equipped with Luxemburg and Orlicz norm, respectively.

• Referencias bibliográficas
  • D. Amir, On Jung’s constant and related constants in normed linear spaces, Pacific J. Math. 118 (1985), 1–15.
  • V.J. Berdyshev, A relation between Jackson inequality and a geometrical problem, Math. Notes 3 (1963), 206–213.
  • F. Bohnenblust, Convex regions and projections in Minkowski spaces, Ann. of Math. 39 (1938), 301–308.
  • B. Grünbaum, On some covering and intersection properties in Minkowski spaces, Pacific J. Math. 9 (1959), 487–494.
  • H.W.E. Jung, Über die kleinste Kugel, die eine räumliche Figur einschisst, J. Reine Angew. Math. 123 (1901), 241–257.
  • S.A. Pichugov, The Jung constant of the space $L^p$, Math. Notes 43 (1988), 348–354.
  • M.M. Rao and Z.D. Ren, Applications of Orlicz Spaces, Marcel Dekker, New York, 2002.
  • Z.D. Ren and S.T. Chen, Jung constants of Orlicz function spaces, Collect. Math. 48 (1997), 743–771.
  • Y.Q. Yan, Some results on packing in Orlicz sequence spaces, Studia Math. 147 (2001), 73–88.
  • T. Zhang, Jung Constants of Orlicz Sequence Spaces, PhD. Dissertation, Suzhou Univ., Suzhou, P.R. China, 2000.