On regularity and weak regularity of functions generating Marcinkiewicz spaces

Marcinkiewicz spaces play an important role in the real interpolation of linear oper­ ators. In view of well-known Calderon interpolation theorem, the Marcinkiewicz spaces serve as “elementary cells” of interpolation, densly packing each space that can be interpo­ lated between L°°(0, 1) and L l (0, 1).