1. Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces
- Creator:
- Yan, Xuefang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- non-negative self-adjoint operator, Stein's square function, Bochner-Riesz means, Davies-Gaffney estimate, and molecule Hardy space
- Language:
- English
- Description:
- 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 ${\rm e}^{-tL}$ 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 $0<p\leq 1$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public