Weak (p, q) Inequalities for Fractional Integral Operators on Generalized Morrey Spaces of Non-Homogeneous Type

Denny Ivanal Hakim and Hendra

Abstract

In this paper, we prove weak (p, q) inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces for 1 ≤ p < q < ∞. The proof involves an inequality for the modified HardyLittlewood maximal operator and the Chebyshev inequality. Our results generalize those obtained by Garcia-Cuerva and Gatto [1] and also extend those by Sihwaningrum et al. [5].