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On the Principle of Duality in Lorentz Spaces

Published online by Cambridge University Press:  20 November 2018

M. L. Gol'Dman ,
H. P. Heinig  and
V. D. Stepanov
M. L. Gol'Dman
Affiliation:
Moscow Institute of Radiotechnology, Electronics and Automation Krupskaja 8-1-187 Moscow 117311 Russia email: e-mail: seulydia@glas.apc.org
H. P. Heinig
Affiliation:
Department of Mathematics and Statistics McMaster University, Hamilton, Ontario L8S 4K1 email: e-mail:Heinig@mcmaster.ca
V. D. Stepanov
Affiliation:
Computer Center of the Far-Eastern Branch of the Russian Academy of Sciences Shelest 118-205 Khabarovsk 6800042 email: e-mail:1600@as.khabarovsk.su
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Abstract

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characterization of the spaces dual to weighted Lorentz spaces are given by means of reverse Hölder inequalities (Theorems 2.1, 2.2). This principle of duality is then applied to characterize weight functions for which the identity operator, the Hardy-Littlewood maximal operator and the Hilbert transform are bounded on weighted Lorentz spaces.

Keywords

47B3842B2046E3026D15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 5 , 01 October 1996 , pp. 959 - 979
Copyright
Copyright © Canadian Mathematical Society 1996

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