Heat kernels of generalized degenerate Schrödinger operators and Hardy spaces

The Anh Bui, Tan Duc Do, Nguyen Ngoc Trong

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Let [Formula presented] be the generalized degenerate Schrödinger operator in Lw2(Rd) with d ≥ 3 with suitable weight w and measure μ. The main aim of this paper is threefold. Firstly, we obtain an upper bound for the fundamental solution of the operator L. Secondly, we prove some estimates for the heat kernel of L including an upper bound, the Hölder continuity and a comparison estimate. Finally, we apply the results to study the maximal function characterization for the Hardy spaces associated to the critical function generated by the operator L.

    Original languageEnglish
    Article number108785
    Pages (from-to)1-49
    Number of pages49
    JournalJournal of Functional Analysis
    Volume280
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2021

    Keywords

    • Generalized degenerate Schrödinger operator
    • Fundamental solution
    • Heat kernel
    • Hardy space

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