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Three geometric constants for Morrey spaces

Yoshihiro Sawano|Eder Kikianty|Hendra Gunawan|Christopher Schwanke
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1569-1575|DOI 10.4134/BKMS.b190010

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키워드

Morrey spacesDunkl-Williams constantJames constantvon Neumann-Jordan constant
주제분류수학

초록

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 $L^1$ and $L^\infty$ spaces.

Abstract

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 $L^1$ and $L^\infty$ spaces.

참고문헌 (10)

  1. David R. Adams, "Morrey spaces in harmonic analysis", Arkiv för Matematik, 50(2), pp.201~230 (2012), International Press of Boston[DOI]
  2. E. Casini, "About some parameters of normed linear spaces", Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8), 80(1-2), pp.11~15 (1986)
  3. C. F. Dunkl, "A Simple Norm Inequality", The American Mathematical Monthly, 71(1), pp.53~54 (1964), JSTOR[DOI]
  4. J. Gao, "On the geometry of spheres in normed linear spaces", J. Austral. Math. Soc. Ser. A, 48(1), pp.101~112 (1990)
  5. Hendra Gunawan, "Discrete Morrey spaces and their inclusion properties", Mathematische Nachrichten, 291(8-9), pp.1283~1296 (2018), Wiley[DOI]
  6. Robert C. James, "Uniformly Non-Square Banach Spaces", The Annals of Mathematics, 80(3), pp.542~550 (1964), JSTOR[DOI]
  7. A. Jiménez-Melado, "The Dunkl–Williams constant, convexity, smoothness and normal structure", Journal of Mathematical Analysis and Applications, 342(1), pp.298~310 (2008), Elsevier BV[DOI]
  8. P. Jordan, "On Inner Products in Linear, Metric Spaces", The Annals of Mathematics, 36(3), pp.719~723 (1935), JSTOR[DOI]
  9. Mikio Kato, "On James and Jordan–von Neumann Constants of Lorentz Sequence Spaces", Journal of Mathematical Analysis and Applications, 258(2), pp.457~465 (2001), Elsevier BV[DOI]
  10. Y. Sawano, "Harmonic analysis and nonlinear partial dierential equations" (2011), Res. Inst. Math. Sci. (RIMS)

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