摘要
Let (X, d,μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2(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 HL^p(X) to L^p(X) for all 0 〈 p ≤ 1.
Let (X, d,μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2(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 HL^p(X) to L^p(X) for all 0 〈 p ≤ 1.