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Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type

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Abstract

The aim of this article is to develop the theory of product Hardy spaces associated with operators which possess the weak assumption of Davies–Gaffney heat kernel estimates, in the setting of spaces of homogeneous type. We also establish a Calderón–Zygmund decomposition on product spaces, which is of independent and use it to study the interpolation of these product Hardy spaces. We then show that under the assumption of generalized Gaussian estimates, the product Hardy spaces coincide with the Lebesgue spaces, for an appropriate range of p.

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Acknowledgments

P. Chen, X.T. Duong, J. Li and L.A. Ward are supported by the Australian Research Council (ARC) under Grant No. ARC-DP120100399. L.X. Yan is supported by the NNSF of China, Grant Nos. 10925106 and 11371378. P. Chen is partially supported by the NNSF of China, Grant No. 11501583. Part of this work was done during L.X. Yan’s stay at Macquarie University and visit to the University of South Australia. L.X. Yan would like to thank Macquarie University and the University of South Australia for their hospitality.

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Peng Chen & Lixin Yan

  2. School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, SA, 5095, Australia

    Peng Chen & Lesley A. Ward

  3. Department of Mathematics, Macquarie University, North Ryde, NSW, 2109, Australia

    Xuan Thinh Duong & Ji Li

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  1. Peng Chen
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Correspondence to Xuan Thinh Duong.

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Chen, P., Duong, X.T., Li, J. et al. Product Hardy spaces associated to operators with heat kernel bounds on spaces of homogeneous type. Math. Z. 282, 1033–1065 (2016). https://doi.org/10.1007/s00209-015-1577-6

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