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

Title:

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

Creator:

Yan, Xuefang

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a0b6a3ba-2d52-4859-9f2f-1ce648916abd
uuid:a0b6a3ba-2d52-4859-9f2f-1ce648916abd

Subject:

non-negative self-adjoint operator, Stein's square function, Bochner-Riesz means, Davies-Gaffney estimate, and molecule Hardy space

Type:

model:article and TEXT

Format:

bez média and svazek

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 $0<p\leq 1$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

61-82

Source:

Czechoslovak Mathematical Journal | 2015 Volume:65 | Number:1

Harvested from:

CDK

Metadata only:

false