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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