Some Estimates for Maximal Bochner-Riesz Means on Musielak-Orlicz Hardy Spaces

Let phi: Double-struck capital Rn x [0, infinity) -> [0, infinity) satisfy that phi(x, center dot), for any given x is an element of Rn, is an Orlicz function and phi(center dot, t) is a Muckenhoupt A infinity weight uniformly in t is an element of (0, infinity). The Musielak-Orlicz Hardy space H-phi(Double-struck capital R-n) is defined to be the space of all tempered distributions whose grand maximal functions belong to the Musielak-Orlicz space L-phi(Double-struck capital R-n). In this paper, the authors establish the boundedness of maximal Bochner-Riesz means T*(delta) from H-phi(Double-struck capital R-n) to WL phi(Double-struck capital R-n) or L-phi(Double-struck capital R-n). These results are also new even when phi(x, t):= phi(t) for all (x, t) is an element of Double-struck capital R-n x [0, infinity), where phi is an Orlicz function.