Gradient Estimate for the Heat Kernel on Some Fractal-Like Cable Systems and Quasi-Riesz Transforms

2021/03/18 by Baptiste Devyver, Emmanuel Russ, Devyver, Baptiste +3 · 3 citations
Computer Science · Mathematics · #28A80 #35K08 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Fractal #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Heat kernel #Kernel (algebra) #Mathematical analysis #Mathematics #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations #Pointwise #Pure mathematics #Riesz transform #math.AP #math.DG #math.FA #math.MG #msc:28A80 #msc:35K08

paper · pdf · doi:10.48550/arxiv.2103.10181

published in arXiv (Cornell University) (Cornell University) · 30 pages

openalex publication_date 2021/03/18 · arxiv created 2021/06/22 · arxiv updated 2021/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We give pointwise upper estimate for the gradient of the heat kernel on some fractal-like cable systems including the Vicsek and the Sierpiński cable systems. Applications to L^p-boundedness of quasi-Riesz transforms are derived.

Citations

• On the parabolic kernel of the Schrödinger operator

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