Three geometric constants for morrey spaces
Gunawan H.a, Kikianty E.b, Sawano Y.c,d, Schwanke C.e,f
a Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, 40132, Indonesia
b Department of Mathematics and Applied Mathematics, University of Pretoria Private Bag X20, Hatfield, 0028, South Africa
c Department of Mathematics and Information Science, Tokyo Metropolitan University Minamioosawa, Tokyo, 192-0364, Japan
d Department of Mathematics Analysis and the Theory of functions Peoples’ Friendship University of Russia, Moscow, Russian Federation
e Department of Mathematics, Lyon College, Batesville, 72501, United States
f Unit for BMI North-West University Private Bag X6001, Potchefstroom, 2520, South Africa
Abstract
©2019 Korean Mathematial Soiety.In this paper we calculate three geometric constants, namely the von Neumann-Jordan constant, the James constant, and the Dunkl-Williams constant, for Morrey spaces and discrete Morrey spaces. These constants measure uniformly nonsquareness of the associated spaces. We obtain that the three constants are the same as those for L1 and L∞ spaces.
Author keywords
Indexed keywords
Dunkl-Williams constant,James constant,Morrey spaces,Von Neumann-Jordan constant
Funding details
[{‘$’: ‘The first author is supported by ITB Research and Innovation Program 2019. The second author is supported by National Research Foundation of South Africa, Grant No. 109297. The third author is supported by Grant-in-Aid for Scientific Research (C) (Grant No. 16K05209), the Japan Society for the Promotion of Science, and by People?s Friendship University of Russia.’}, {‘$’: ‘Received January 4, 2019; Accepted July 8, 2019. 2010 Mathematics Subject Classification. Primary 46B20. Key words and phrases. Morrey spaces, Dunkl-Williams constant, James constant, von Neumann-Jordan constant. The first author is supported by ITB Research and Innovation Program 2019. The second author is supported by National Research Foundation of South Africa, Grant No. 109297. The third author is supported by Grant-in-Aid for Scientific Research (C) (Grant No. 16K05209), the Japan Society for the Promotion of Science, and by People’s Friendship University of Russia.’}]