The Packing Spheres Constant for a Class of Separable Orlicz Function Spaces

Xisheng Yu

Abstract


Few results have been obtained on the packing spheres constant or exact formula for separable Orlicz function spaces
(Yang, 2002, P.895-899, Ye, 1987, P.487-493). In this paper, by using the continuity of ideal space norm, we firstly
proved that simple function class is dense in L?? function space. This is a necessary condition of interpolation theorem.
Hence, the exact value of packing sphere for a class of sparable Orlicz function spaces (with two kinds of norm) is
obtained. Secondly, for the space L??[0, 1] discussed in (Yang, 2002, P.895-899), we propose the following conjecture: the
L?? [0, 1] space is actually the Lp[0, 1] space, therefore, the results obtained there is actually the proved results in Lp space.

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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