Weak type estimates of Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces

Abstract

This paper proves the weak type estimates of the Hardy–Littlewood maximal operator on local Morrey spaces associated with ball quasi-Banach function spaces. As an application, we further obtain the weak type estimates of the Hardy–Littlewood maximal operator on the local Morrey spaces with variable exponents and the homogeneous Herz-type spaces with variable exponents.

Keywords

• Ball quasi-Banach function spaces
• Local Morrey spaces
• Variable exponents
• Weak-type estimates
• Maximal operator