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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.
- Generalized degenerate Schrödinger operator
- Fundamental solution
- Heat kernel
- Hardy space