The boundedness of the Hardy–Littlewood maximal operator on Orlicz–Lorentz–Karamata spaces

Abstract. In this paper, we prove that the Hardy–Littlewood maximal operator is bounded on the Orlicz–Lorentz–Karamata space \(L_{\Phi,q,b}(\mathbb{R}^n)\). More precisely, we give a sufficient condition for the boundedness of the Hardy–Littlewood maximal operator on \(L_{\Phi,q,b}(\mathbb{R}^n)\) when a Young function \(\Phi\in\nabla_2\), \(1\leq q\leq\infty\) and \(b\) is a slowly varying function.