Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
mixed Morrey spaces; von Neumann-Jordan constant; James constant; Dunkl-Williams constant; uniformly convex; uniformly nonsquare
Summary:
We compute several geometric constants for mixed Morrey spaces, namely von Neumann-Jordan constant, James constant, and Dunkl-Williams constant. Through the values of the constants that we obtain, we know that mixed Morrey spaces are not uniformly convex nor uniformly nonsquare. Our result extends previous results on geometric constants for discrete Morrey spaces.
References:
[1] Adams, D. R.: Morrey Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham (2015). DOI 10.1007/978-3-319-26681-7 | MR 3467116 | Zbl 1339.42001
[2] Casini, E.: About some parameters of normed linear spaces. Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 80 (1986), 11-15. MR 0944367 | Zbl 0637.46019
[3] Clarkson, J. A.: Uniformly convex spaces. Trans. Am. Math. Soc. 40 (1936), 396-414. DOI 10.1090/S0002-9947-1936-1501880-4 | MR 1501880 | Zbl 0015.35604
[4] Cui, Y., Hudzik, H., Wisł{a}, M., Wlaźak, K.: Non-squareness properties of Orlicz spaces equipped with the $p$-Amemiya norm. Nonlinear Anal., Theory Methods Appl., Ser. A 75 (2012), 3973-3993. DOI 10.1016/j.na.2012.02.014 | MR 2914585 | Zbl 1247.46015
[5] Dunkl, F. C., Williams, K.: A simple norm inequality. Am. Math. Mon. 71 (1964), 53-54. DOI 10.2307/2311304 | MR 1532478 | Zbl 0178.16202
[6] Gao, J., Lau, K.-S.: On the geometry of spheres in normed linear spaces. J. Aust. Math. Soc., Ser. A 48 (1990), 101-112. DOI 10.1017/S1446788700035230 | MR 1026841 | Zbl 0687.46012
[7] Gunawan, H., Hakim, D. I., Ifronika, Neswan, O.: Inclusion and geometric properties of mixed Morrey double-sequence spaces. Bull. Malays. Math. Sci. Soc. (2) 47 (2024), Article ID 132, 12 pages. DOI 10.1007/s40840-024-01723-2 | MR 4764517 | Zbl 1545.42018
[8] Gunawan, H., Kikianty, E., Sawano, Y., Schwanke, C.: Three geometric constants for Morrey spaces. Bull. Korean Math. Soc. 56 (2019), 1569-1575. DOI 10.4134/BKMS.b190010 | MR 4037393 | Zbl 1441.46015
[9] James, R. C.: Uniformly non-square Banach spaces. Ann. Math. (2) 80 (1964), 542-550. DOI 10.2307/1970663 | MR 0173932 | Zbl 0132.08902
[10] Jiménez-Melado, A., Llorens-Fuster, E., Mazcuñán-Navarro, E. M.: The Dunkl-Williams constant, convexity, smoothness and normal structure. J. Math. Anal. Appl. 342 (2008), 298-310. DOI 10.1016/j.jmaa.2007.11.045 | MR 2440797 | Zbl 1151.46009
[11] Jordan, P., Neumann, J. von: On inner products in linear, metric spaces. Ann. Math. (2) 36 (1935), 719-723. DOI 10.2307/1968653 | MR 1503247 | Zbl 0012.30702
[12] Nogayama, T.: Mixed Morrey spaces. Positivity 23 (2019), 961-1000. DOI 10.1007/s11117-019-00646-8 | MR 3993567 | Zbl 1428.42032
[13] Ragusa, M. A., Scapellato, A.: Mixed Morrey spaces and their applications to partial differential equations. Nonlinear Anal., Theory Methods Appl., Ser. A 151 (2017), 51-65. DOI 10.1016/j.na.2016.11.017 | MR 3596670 | Zbl 1368.46031
[14] Sawano, Y., Fazio, G. Di, Hakim, D. I.: Morrey Spaces: Introduction and Applications to Integral Operators and PDE's. Volume I. CRC Press, Boca Raton (2020). DOI 10.1201/9780429085925 | MR 4288177 | Zbl 1482.42002
[15] Sawano, Y., Fazio, G. Di, Hakim, D. I.: Morrey Spaces: Introduction and Applications to Integral Operators and PDE's. Volume II. CRC Press, Boca Ratan (2020). DOI 10.1201/9781003029076 | MR 4288178 | Zbl 1482.42001
[16] Takahashi, Y., Kato, M.: von Neumann-Jordan constant and uniformly non-square Banach spaces. Nihonkai Math. J. 9 (1998), 155-169. MR 1661080 | Zbl 1015.46010
[17] Tarigan, M. O. I. P., Gunadi, R., Hakim, D. I., Ifronika: Inclusion of mixed Morrey spaces. Adv. Oper. Theory 8 (2023), Article ID 16, 13 pages. DOI 10.1007/s43036-022-00241-x | MR 4537544 | Zbl 1506.42028
[18] Wu, S., Yang, D., Yuan, W.: Interpolations of mixed-norm function spaces. Bull. Malays. Math. Sci. Soc. (2) 45 (2022), 153-175. DOI 10.1007/s40840-021-01187-8 | MR 4351127 | Zbl 1486.42039
Partner of
EuDML logo