The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup

Abstract

AbstractIn this paper, we discuss various maximal functions on the Laguerre hypergroup K including the heat maximal function, the Poisson maximal function, and the Hardy–Littlewood maximal function which is consistent with the structure of hypergroup of K. We shall establish the weak type (1, 1) estimates for these maximal functions. The Lp estimates for p > 1 follow fromthe interpolation. Some applications are included.