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MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH non-negative self-adjoint operatorS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

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Acta Mathematica Scientia 2024年第2期44卷 484-514页

作者：林孝盛杨大春杨四辈袁文 Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing100875China School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild *** HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by *** this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy *** results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey ***,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

关键词： Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function

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BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO operatorS ON HARDY SPACES

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Acta Mathematica Scientia 2014年第3期34卷 891-904页

作者：闫雪芳 Department of Mathematics Sun Yat-sen (Zhongshan) University College of Mathematics and Information Science Heibei Normal University

Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（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 Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.

关键词： Stein's square function non-negative self-adjoint operator Hardy spaces Davies- Gaffney estimate Plancherel type estimate

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A local version of Hardy spaces associated with operators on metric spaces

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Science China Mathematics 2013年第2期56卷 315-330页

作者： GONG RuMing LI Ji YAN LiXin School of Mathematics and Information Science Guangzhou University Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes Guangzhou University Department of Mathematics Sun Yat-sen University

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 second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.

关键词： local Hardy space non-negative self-adjoint operator semigroups local (1 p)-atoms Moser typelocal boundedness condition space of homogeneous type

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