Abstract and Applied Analysis
Volume 6 (2001), Issue 2, Pages 101-114

Extension of the best approximation operator in Orlicz spaces and weak-type inequalities

Sergio Favier and Felipe Zò

Instituto de Matemática Aplicada San Luis, Universidad Nacional de San Luis, Consejo Nacional de Investigaciones Científicas y Técnicas, Avenida Ejército de los Andes 950, San Luis 5700, Argentina

Received 19 December 2000

Copyright © 2001 Sergio Favier and Felipe Zò. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider an extension of the best approximation operator from an Orlicz space Lφ to the space Lφ, where φ denotes the derivative of φ, and we prove a weak-type inequality in this space. Further, we obtain some strong inequalities for suitable Lψ spaces.