数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
3期
891-904
,共14页
Stein’s square function%non-negative self-adjoint operator%Hardy spaces%Davies-Gaffney estimate%Plancherel type estimate
Let (X, d, μ) be a metric measure space endowed with a metric d and a nonneg-ative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup e-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein’s square function Gδ(L) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HpL(X) to Lp(X) for all 0<p≤1.
