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Boundedness of Some Integral Operators

Published online by Cambridge University Press:  20 November 2018

María J. Carro  and
Javier Soria
María J. Carro*
Affiliation:
Departament de Matematiques Univ. Autonoma de Barcelona 08193 Bellatera Barcelona, Spain
Javier Soria*
Affiliation:
Departament de Matematica Aplicada i Analisi Universitat de Barcelona08071 Barcelona Spain, e-mail: soria@cerber.ub.es
*
Current address: Departament de Matematica Aplicada i Analisi Universitat de Barcelona 08071 Barcelona Spain, e-mail: carro@cerber.ub.es
Current address: Departament de Matematica Aplicada i Analisi Universitat de Barcelona 08071 Barcelona Spain, e-mail: carro@cerber.ub.es
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Abstract

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We apply the expression for the norm of a function in the weighted Lorentz space, with respect to the distribution function, to obtain as a simple consequence some weighted inequalities for integral operators.

Keywords

42B25

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 6 , 01 December 1993 , pp. 1155 - 1166
Copyright
Copyright © Canadian Mathematical Society 1993

Footnotes

This work has been partially supported by DGICYT grant: PB91-0259

References

1. Andersen, K., Weighted generalized Hardy inequalities for nonincreasing functions, Canad. J. Math. 43 (1991), 1121.1135.Google Scholar
2. Arino, M. and Muckenhoupt, B., Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing function, Trans. Amer. Math. Soc. 320(1990), 727–735.Google Scholar
3. Bennet, C. and Sharpley, R., Interpolation of operators, Academic Press, 1988.Google Scholar
4. Carro, M.J. and Soria, J., Weighted Lorentz spaces and the Hardy operator, Jour. Funct. Anal, 112(1993), 480–494.Google Scholar
5. Martin, F. J.-Reyes and Sawyer, E., Weighted inequalities for Riemann-Liouville fractional integrals of order one and greater, Proc. Amer. Math. Soc. 106(1989), 727–733.Google Scholar
6. Neugebauer, C.J., Weighted norm inequalities for general operators of monotone functions, Publi. Mat. 35(1991), 429–447.Google Scholar
7. Sawyer, E., Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96(1990), 145—158.Google Scholar