The non-commutative hardy-littlewood maximal operator on non-commutative lorentz spaces

Abstract

In this work we study the non-commutative Hardy-Littlewoodmaximal operator on Lorentz spacesofτ-measurable operators. Non-commutative maximal inequalities were studied, in particular,in [1–3]. Another version of the (non-commutative) Hardy-Littlewood maximal operator was in-troduced by T. Bekjan [4]. Later J. Shao investigated the Hardy-Littlewood maximal operator onnon-commutative Lorentz spaces associated with finite atomless von Neumann algebra (see [5]).

Keywords

• cesaro operator
• hardy-littlewood maximal operator
• lorentz space