Abstract and Applied Analysis
Volume 6 (2001), Issue 2, Pages 101-114
doi:10.1155/S1085337501000446
Extension of the best approximation operator in Orlicz spaces and weak-type inequalities
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.
Abstract
We consider an extension of the best approximation operator from
an Orlicz space L φ
to the space L φ′, 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 L ψ spaces.