Jan Krejvc'i

Operators on Orlicz sequence spaces and $\Delta_2$-fundamentality

A classical result states that the Hardy--Littlewood maximal operator is bounded on an Orlicz space $L^A(\mathbb{R}^n)$ if and only if its conjugate Young function $\tilde{A}$ satisfies the $\Delta_2$-condition. The same condition also characterizes the boundedness on $L^A(0,\infty)$ of the Hardy averaging operator. We...