LAUSR

In this paper, we give the definition of local variable MorreyLorentz spaces Mloc p(·),q(·),λ(R n) which are a new class of functions. Also, we prove the boundedness of the Hardy-Littlewood maximal operator M and Calderón-Zygmund operators T on these spaces including the class of sublinear operators T0 generated by CalderónZygmund operators. Finally, we apply these results to the BochnerRiesz operator Bδ r , identity approximation Aε and the Marcinkiewicz operator μΩ on the spaces M loc p(·),q(·),λ(R n). AMS Subject Classification: Primary 42B25, 42B35; Secondary 47G10.