Vector-Valued Inequalities in the Morrey Type Spaces

Abstract

We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spaces , ( ) when 1 ≤ < ∞ and 0 < < 1, and in the generalized Morrey spaces ,Φ for 1 ≤ < ∞, where Φ is a growth function on (0, ∞) satisfying the doubling condition.