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

摘要

Let Φ : R~n × [0,∞) → [0, ∞) satisfy that Φ(x, ·). for anY given x∈R~n, is an Orlicz function and Φ(·, t) is a Muckenhoupt A_∞ weight uniformly in t ∈ (0, ∞). The Musielak-Orlicz Hardy space H~Φ(R~n) is defined to be the space of all tempered distributions whose grand maximal functions belong to the Musielak-Orlicz space L~Φ(R~n). In this paper, the authors establish the boundedness of maximal Bochner-Riesz means T~δ_* from H~Φ(R~n) to WL~Φ(R~n) or L~Φ(R~n). These results are also new even when Φ(x, t) := Φ(t) for all (x,t) ∈ Rn × [0, ∞), where Φ is an Orlicz function.