Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-02T23:44:53.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimates for polynomial norms on Lp(μ) spaces

Published online by Cambridge University Press:  24 October 2008

I. Sarantopoulos
I. Sarantopoulos
Affiliation:
Department of Mathematics and Statistics, Brunel University, England and Department of Mathematics, National Technical University of Athens, Greece
Get access Rights & Permissions [Opens in a new window]

Abstract

If L is a symmetric m-linear form on a Banach space and L^ is the associated polynomial then

For special choices of Banach space this inequality can be improved. This has been done by Harris [5] in the case of the Lp(μ) spaces. In this paper we improve his estimates and disprove one of his conjectures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 263 - 271
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Banach, S.. Über homogene polynome in (L 2). Studia Math. 7 (1938), 36–44.Google Scholar
[2]Bergh, J. and Löfström, J.. Interpolation Spaces, An Introduction. Grundlehren der Math., Band 223 (Springer-Verlag, 1976).CrossRefGoogle Scholar
[3]Bochnak, J. and Siciak, J.. Polynomials and multilinear mappings in topological vector spaces. Studia Math. 39 (1971), 59–76.CrossRefGoogle Scholar
[4]Dineen, S.. Complex Analysis in Locally Convex Spaces. Mathematics Studies, vol. 57 (North Holland, 1981).CrossRefGoogle Scholar
[5]Harris, L. A.. Bounds on the derivatives of holomorphic functions of vectors. Colloque d'analyse, Rio de Janeiro, 1972, ed. Nachbin, L.. Act. Sc. et Ind. no. 1367 (Hermann, 1975), pp. 145–163.Google Scholar
[6]Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces. Springer Lecture Notes in Math., vol. 338 (Springer-Verlag, 1973).Google Scholar
[7]Martin, R. S.. Thesis, California Institute of Technology (1932).Google Scholar
[8]Rudin, W.. Real and Complex Analysis (McGraw-Hill, 1974).Google Scholar
[9]The Scottish Book (Mathematics from the Scottish Café), ed. Mauldin, R. D. (Birkhäuser, 1981).Google Scholar
[10]Tonge, A. M.. Polarization and the complex Grothendieck inequality. Math. Proc. Cambridge Philos. Soc. 95 (1984), 313–318.CrossRefGoogle Scholar
[11]Williams, L. and Wells, J.. L pinequalities. J. Math. Anal. Appl. 64 (1978), 518–529.CrossRefGoogle Scholar