Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces

Czechoslovak Mathematical Journal

Xuefang ¹ 

[1] College of Mathematics and Information Science, Heibei Normal University, No. 20 South 2nd Ring Road (East), Shijiazhuang, Hebei Prov., 050024, P. R. China

关键词: non-negative self-adjoint operator;    Stein's square function;    Bochner-Riesz means;    Davies-Gaffney estimate;    molecule Hardy space;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Let $(X, d, \mu)$ be a metric measure space endowed with a distance $d$ and a nonnegative Borel doubling measure $\mu$. Let $L$ be a non-negative self-adjoint operator of order $m$ on $L^2(X)$. Assume that the semigroup $ e^{-tL}$ generated by $L$ satisfies the Davies-Gaffney estimate of order $m$ and $L$ satisfies the Plancherel type estimate. Let $H^p_L(X)$ be the Hardy space associated with $L.$ We show the boundedness of Stein's square function ${\mathcal G}_{\delta}(L)$ arising from Bochner-Riesz means associated to $L$ from Hardy spaces $H^p_L(X)$ to $L^p(X)$, and also study the boundedness of Bochner-Riesz means on Hardy spaces $H^p_L(X)$ for $0

【 授权许可】

Unknown