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

Authors
  • Liu, Suying1
  • Zhang, Chao2
  • 1 Northwest Polytechnical University, Xi’an, 710072, China , Xi’an (China)
  • 2 Zhejiang Gongshang University, Hangzhou, 310018, China , Hangzhou (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Sep 20, 2020
Volume
40
Issue
5
Pages
1215–1228
Identifiers
DOI: 10.1007/s10473-020-0504-z
Source
Springer Nature
Keywords
License
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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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