BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

doi:10.1016/S0252-9602(14)60057-6

Abstract

Abstract:

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 G_δL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces H^p_L(X) to L^p(X) for all 0 < p ≤1.

Key words: Stein´s square function, non-negative self-adjoint operator, Hardy spaces, Davies-Gaffney estimate, Plancherel type estimate

CLC Number:

42B15

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.

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