Maximal and Calderon-Zygmund Operators on the Local Variable Morrey-Lorentz Spaces and Some Applications

Abstract

In this paper, we give the definition of local variable Morrey-Lorentz spaces M-p(.),q(.),lambda(loc) (R-n) which are a new class of functions. Also, we prove the boundedness of the Hardy- Littlewood maximal operator M and Calderon- Zygmund operators T on these spaces. Finally, we apply these results to the Bochner-Riesz operator B-d(delta), identity approximation Ae and the Marcinkiewicz operator mu(Omega) on the spaces M-p(.),q(.),lambda(loc) (R-n) .