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Boundedness of Variation Operators Associated with the Heat Semigroup Generated by High Order Schrödinger Type Operators

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Abstract

In this article, we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrödinger type operator (−Δ)2 + V2 in ℝn(n ≥ 5) with V being a nonnegative potential satisfying the reverse Hölder inequality. Furthermore, we prove the boundedness of the variation operators on associated Morrey spaces. In the proof of the main results, we always make use of the variation inequalities associated with the heat semigroup generated by the biharmonic operator (−Δ)2.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwest Polytechnical University, Xi’an, 710072, China

    Suying Liu

  2. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China

    Chao Zhang

Authors
  1. Suying Liu
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  2. Chao Zhang
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Correspondence to Chao Zhang.

Additional information

The first author was supported by the National Natural Science Foundation of China (11701453) and Fundamental Research Funds for the Central Universities (31020180QD05). The second author was supported by the National Natural Science Foundation of China (11971431, 11401525), the Natural Science Foundation of Zhejiang Province (LY18A010006), and the first Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics).

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Liu, S., Zhang, C. Boundedness of Variation Operators Associated with the Heat Semigroup Generated by High Order Schrödinger Type Operators. Acta Math Sci 40, 1215–1228 (2020). https://doi.org/10.1007/s10473-020-0504-z

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  • DOI: https://doi.org/10.1007/s10473-020-0504-z

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