Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T06:33:43.653Z Has data issue: false hasContentIssue false
  • English
  • Français

K-ENVELOPES FOR REAL INTERPOLATION METHODS

Published online by Cambridge University Press:  02 August 2012

MING FAN
MING FAN*
Affiliation:
School of Technology and Business Studies, Dalarna University, 781 88 Borlänge, Sweden e-mail: fmi@du.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the KΦ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.

Keywords

Primary 46B7046M35Secondary 46B2546E30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 55 , Issue 2 , May 2013 , pp. 293 - 307
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

REFERENCES

1.Bennett, C. and Sharpley, R., Interpolation of operators, pure and applied mathmatics, vol. 129 (Academic Press, New York, 1988).Google Scholar
2.Bergh, J. and Löfström, J., Interpolation spaces, Grundlehren Math. Wiss., vol. 223, (Springer-Verlag, New York, 1976).Google Scholar
3.Brudnyi, Y. A. and Kruglyak, N. Ja., Interpolation functors and interpolation spaces (North-Holland, Amsterdam, Netherlands, 1991).Google Scholar
4.Cobos, F., Cwikel, M. and Matos, P., Best possible compactness results of Lions-Peetre type, Proc. Edin. Math. Soc. 44 (2001), 153–173.CrossRefGoogle Scholar
5.Cobos, F., Fernández-Cabrera, L. and Martínez, A., Abstract K and J spaces and measure of non-compactness, Math. Nachr. 280 (2007), 1698–1708.CrossRefGoogle Scholar
6.Fan, M., Interpolation methods of constants and means with quasi–power function parameters, Math. Scand. 88 (2001), 79–95.CrossRefGoogle Scholar
7.Fan, M., Lions-Peetre's interpolation methods associated with quasi-power functions and some applications, Rocky Mount. J. Math. 36 (2006), 1487–1510.Google Scholar
8.Haroske, D. D., Envelopes and sharp embeddings of function spaces, Chapman & Hall/CRC Research Notes in Math., vol. 437 (Chapman & Hall/CRC, Boca Raton, FL, 2006).Google Scholar
9.Haroske, D. D., Envelope function in real interpolation spaces, Contemp. Math. 445 (2007), 93–102.Google Scholar
10.Pustylnik, E., Embedding functions and their role in interpolation theory, Abst. Appl. Anal. 1 (1996), 305–325.CrossRefGoogle Scholar
11.Pustylnik, E., On some properties of generalized Marcinkiewicz spaces, Studia Math. 144 (2001), 227–243.CrossRefGoogle Scholar
12.Pustylnik, E., Ultrasymmetric spaces, J. Lond. Math. Soc. 68 (2) (2003), 165–182.Google Scholar