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Weighted L p estimates for the area integral associated to self-adjoint operators

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Abstract

This article is concerned with some weighted norm inequalities for the so-called horizontal (i.e., involving time derivatives) area integrals associated to a non-negative self-adjoint operator satisfying a pointwise Gaussian estimate for its heat kernel, as well as the corresponding vertical (i.e., involving space derivatives) area integrals associated to a non-negative self-adjoint operator satisfying in addition a pointwise upper bounds for the gradient of the heat kernel. As applications, we obtain sharp estimates for the operator norm of the area integrals on \({L^p(\mathbb{R}^N)}\) as p becomes large, and the growth of the A p constant on estimates of the area integrals on the weighted L p spaces.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Ruming Gong

  2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Ruming Gong

  3. Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou, 510275, People’s Republic of China

    Lixin Yan

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  1. Ruming Gong
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  2. Lixin Yan
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Correspondence to Lixin Yan.

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Gong, R., Yan, L. Weighted L p estimates for the area integral associated to self-adjoint operators. manuscripta math. 144, 25–49 (2014). https://doi.org/10.1007/s00229-013-0639-5

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  • DOI: https://doi.org/10.1007/s00229-013-0639-5

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