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

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Abstract

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−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 \({g_\delta }(L)\) 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 ⩽ 1.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Heibei Normal University, No. 20 South 2nd Ring Road (East), Shijiazhuang, Hebei Prov., 050024, P.R. China

    Xuefang Yan

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  1. Xuefang Yan
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Correspondence to Xuefang Yan.

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This project was supported by Science and Technology Research of Higher Education in Hebei province (No. Z2014057).

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Yan, X. Boundedness of Stein’s square functions and Bochner-Riesz means associated to operators on hardy spaces. Czech Math J 65, 61–82 (2015). https://doi.org/10.1007/s10587-015-0160-y

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  • DOI: https://doi.org/10.1007/s10587-015-0160-y

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