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The Weighted L p−L q Boundedness of Commutators of Schrödinger Type Operators on the Stratified Lie Group G

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Abstract

Let −Δ G + V be a Schrödinger operator on a stratified Lie group G. Assume that V is a nonegative potential belonging to the reverse Hölder class \(B_{q_{1}}\) for some q 1≥Q/2,where Q is the homogeneous dimension of G. The main aim of this paper is to study the weighted L p−L q estimate for the commutators of the Schrödinger type operators (−Δ G + V)−β V α and (−Δ G + V)−β∇ G V α for certain α and β.

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Acknowledgments

The author would like to thank B.T. Anh for suggesting the topic and for his helpful discussion and suggestions. He also thanks the referees for their useful comments which improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Pedagogy, Ho Chi Minh City, Vietnam

    Nguyen Ngoc Trong

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  1. Nguyen Ngoc Trong
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Correspondence to Nguyen Ngoc Trong.

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Trong, N.N. The Weighted L p−L q Boundedness of Commutators of Schrödinger Type Operators on the Stratified Lie Group G . Vietnam J. Math. 44, 839–856 (2016). https://doi.org/10.1007/s10013-016-0210-2

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  • DOI: https://doi.org/10.1007/s10013-016-0210-2

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