Bochner-Riesz算子在加权弱型Hardy空间上的有界性

The Boundedness of Bochner-Riesz Operators on the Weighted Weak Hardy Spaces

设w是一个Muckenhoupt议函数且WH_w^p(R^n)是加仅的弱型Hardy空间.通过WH_w^p(R^n)的原子分解定理,将证明当0<P≤I及δ>n/p-(n+1)/2时,极大Bochner-Riesz算子T_*~δ是从WH_w^p(R^n)到WL_w^p(R^n)有界的.而且还将证明对于0<P≤1及δ>n/p-(n+1)/2,Bochner-Riesz算子T_R~δ在加权弱型Hardy空间WH_w^p(R^n)上也是有界的.本文的结果即使对于非加,仅情形也是新的.

Let w be a Muckenhoupt weight and WH^pw（R^n） be the weighted weak Hardy spaces. In this paper, by using the atomic decomposition of WH^pw（R^n）, we will show that the maximal Bochner-Riesz operators Tδ＊ are bounded from WH^pw（R^n） to WL^pw（R^n） when 0 〈 p ≤1 and δ 〉 n/p- （n ＋ 1）/2. Moreover, we will also prove that the Bochner-Riesz operators TRδ are bounded on WHP（~n） for 0 〈 p 〈 1 and δ 〉 n/p - （n ＋ 1）/2. Our results are new even in the unweighted case.