2014/06/26 by L. Roncal, Roncal, L., P. R. Stinga +1
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #math.CA
paper · pdf · doi:10.48550/arxiv.1406.6807
7 pages. To appear in Special Functions, Partial Differential Equations and Harmonic Analysis. Proceedings of the conference in honor of Calixto P. Calderón, Roosevelt University at Chicago, November 16-18, 2012. C. Georgakis, A. Stokolos and W. Urbina (eds)
arxiv created 2014/06/26 · openalex publication_date 2014/06/26 · arxiv updated 2014/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we show how to obtain regularity estimates for the fractional Laplacian on the multidimensional torus \mathbbTn from the fractional Laplacian on ℝn. Though at first glance this may seem quite natural, it must be carefully precised. A reason for that is the simple fact that L2 functions on the torus can not be identified with L2 functions on ℝn. The transference is achieved through a formula that holds in the distributional sense. Such an identity allows us to transfer Harnack inequalities, to relate the extension problems, and to obtain pointwise formulas and Hölder regularity estimates.