Weak Orlicz spaces： Some basic properties and their applications to harmonic analysis

We study some basic properties of weak Orlicz spaces and their applications to harmonic analysis. We first discuss the absolute continuity of the quasi-norm and its normality, then prove the boundedness of several maximal operators. We also establish a kind of Marcinkiewicz-type interpolation theorem between weak Orlicz spaces. As applications, the weak type analogues of several classical inequalities in harmonic analysis is obtained.