Acta mathematica scientia, Series B >
BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES
Received date: 2013-06-28
Revised date: 2013-09-29
Online published: 2014-05-20
Let (X, d, μ) be a metric measure space endowed with a metric d and a nonneg-ative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(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 GδL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HpL(X) to Lp(X) for all 0 < p ≤1.
YAN Xue-Fang . BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 891 -904 . DOI: 10.1016/S0252-9602(14)60057-6
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