Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T08:20:53.824Z Has data issue: false hasContentIssue false
  • English
  • Français

Interpolation restricted to decreasing functions and Lorentz spaces*

Published online by Cambridge University Press:  20 January 2009

Joan Cerdà  and
Joaquim Martín
Joan Cerdà
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain, E-mail addresses: cerda@cerber.mat.ub.es, jmartin@cerber.mat.ub.es
Joaquim Martín
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain, E-mail addresses: cerda@cerber.mat.ub.es, jmartin@cerber.mat.ub.es
Rights & Permissions [Opens in a new window]

Extract

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.

For the real interpolation method, we identify the interpolated spaces of couples of classical Lorentz spaces through interpolation of the corresponding weighted Lp-spaces restricted to decreasing functions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 243 - 256
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Andersen, K., Weighted generalized Hardy inequalities for nonincreasing functions, Canad. J. Math. 43 (1991), 1121–1135.CrossRefGoogle Scholar
2.Ariño, M. and Muckenhoupt, B., Maximal functions on classical Lorentz spaces and Hardy's inequality for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727–735.Google Scholar
3.Bennett, C. and Sharpley, R., Interpolation of Operators(Academic Press, 1988).Google Scholar
4.Bergh, J. and Löfström, J., Interpolation spaces. An introduction (Springer Verlag, 1976).CrossRefGoogle Scholar
5.Brudny, Yu. A. and Krugljak, N. Ya., Interpolation Functors and Interpolation Spaces (North-Holland, 1991).Google Scholar
6.Carro, M. J. and Soria, J., Boundedness of some integral operators, Canad. J. Math. 45 (1993), 1155–1166.CrossRefGoogle Scholar
7.Carro, M. J. and Soria, J., Weighted Lorentz Spaces and the Hardy Operator, J. Funct. Anal. 112 (1993), 480–494.CrossRefGoogle Scholar
8.Cerdà, J. and Martín, J., Interpolation of operators on decreasing functions, Math. Scand. 78 (1996), 233–245.CrossRefGoogle Scholar
9.Cerdà, J. and Martín, J., Conjugate Hardy's inequalities with decreasing weights, Proc. Amer. Math. Soc. 126 (1998), 2341–2344.CrossRefGoogle Scholar
10.Freitag, D., Real Interpolation of weighted L*p-spaces, Math. Nachr. 86 (1978),15–18.CrossRefGoogle Scholar
11.García del Amo, A. J., On reverse Hardy's inequality, Collect. Math. 44 (1993), 115–123.Google Scholar
12.Gustavson, J., A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978), 289–305.CrossRefGoogle Scholar
13.Hudzik, H. and Maligranda, L., An interpolation theorem in symmetric function F-spaces, Proc. Amer. Math. Soc., 110 (1990), 89–96.Google Scholar
14.Krein, S. G., Petunin, Ju. I. and Semenov, E. M., Interpolation of Linear Operators (Transl. Math. Monogr. 54, Amer. Math. Soc., 1982).Google Scholar
15.Maligranda, L. and Persson, L. E., Real interpolation between weighted Lp and Lorentz spaces, Bull Pol. Acad. Sci. 35 (1987), 765–778.Google Scholar
16.Merucci, C., Interpolation réelle avec fonction paramètre: réitération et applications aux espaces Λp(Φ) (0 < p ≤∞), C. R. Acad. Sci. Paris 295 (1982), 427–430.Google Scholar
17.Neugebauer, C. J., Some classical operators on Lorentz space, Forum Math. 4 (1992), 135–146.CrossRefGoogle Scholar
18.Sagher, Y., An application of interpolation theory to Fourier series, Studia Math. 38 (1972), 169–181.CrossRefGoogle Scholar
19.Sawyer, E., Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145–158.CrossRefGoogle Scholar
20.Sharpley, R., Spaces Λ2(X) and interpolation, J. Funct. Anal. 11 (1972), 479–513.CrossRefGoogle Scholar
21.Stepanov, V., Integral operators on the cone of monotone functions, J. London Math. Soc. 48 (1993), 465–487.CrossRefGoogle Scholar