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

Xuefang Yan

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 1, page 61-82
  • ISSN: 0011-4642

Abstract

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Let ( X , d , μ ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ . Let L be a non-negative self-adjoint operator of order m on L 2 ( X ) . Assume that the semigroup e - t L generated by L satisfies the Davies-Gaffney estimate of order m and L satisfies the Plancherel type estimate. Let H L p ( X ) be the Hardy space associated with L . We show the boundedness of Stein’s square function 𝒢 δ ( L ) arising from Bochner-Riesz means associated to L from Hardy spaces H L p ( X ) to L p ( X ) , and also study the boundedness of Bochner-Riesz means on Hardy spaces H L p ( X ) for 0 < p ≤ 1 .

How to cite

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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 65.1 (2015): 61-82. <http://eudml.org/doc/270061>.

@article{Yan2015,
abstract = {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 $0<p\le 1$.},
author = {Yan, Xuefang},
journal = {Czechoslovak Mathematical Journal},
keywords = {non-negative self-adjoint operator; Stein's square function; Bochner-Riesz means; Davies-Gaffney estimate; molecule Hardy space},
language = {eng},
number = {1},
pages = {61-82},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces},
url = {http://eudml.org/doc/270061},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Yan, Xuefang
TI - Boundedness of Stein's square functions and Bochner-Riesz means associated to operators on Hardy spaces
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 61
EP - 82
AB - 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 $0<p\le 1$.
LA - eng
KW - non-negative self-adjoint operator; Stein's square function; Bochner-Riesz means; Davies-Gaffney estimate; molecule Hardy space
UR - http://eudml.org/doc/270061
ER -

References

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