The Schrödinger equation in L^p spaces for operators with heat kernel satisfying Poisson type bounds

2020/07/03 by Chen, Peng, Duong, Xuan Thinh, Fan, Zhijie +2
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.01469

Abstract

Let L be a non-negative self-adjoint operator acting on L²(X) where X is a space of homogeneous type with a dimension n. In this paper, we study sharp endpoint L^p-Sobolev estimates for the solution of the initial value problem for the Schrödinger equation, i ∂_t u + L u=0 and show that for all f∈ L^p(X), 1

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