ON THE CONTINUITY OF THE HARDY-LITTLEWOOD MAXIMAL FUNCTION

Abstract

It is concerned with the continuity of the Hardy-Little wood maximal function between the classical Lebesgue spaces or the Orlicz spaces. A new approach to the continuity of the HardyLittlewood maximal function is presented through the observation that the continuity is closely related to the existence of solutions for a certain type of first order ordinary differential equations. It is applied to verify the continuity of the Hardy-Littlewood maximal function from Lp(Rn) to Lq(Rn) for 1 (cid:20) q < p < 1.

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.