Geodesic
Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 61-82

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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 $0$.
DOI : 10.1007/s10587-015-0160-y
Classification : 42B15, 42B25, 47F05
Keywords: non-negative self-adjoint operator; Stein's square function; Bochner-Riesz means; Davies-Gaffney estimate; molecule Hardy space 
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     title = {Boundedness of {Stein's} square functions and {Bochner-Riesz} means associated to operators on {Hardy} spaces},
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Yan, Xuefang. Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 1, pp. 61-82. doi: 10.1007/s10587-015-0160-y

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