Sharp Adams type inequalities for the fractional Laplace-Beltrami operator on noncompact symmetric spaces

2021/06/16 by Mithun Bhowmik, Bhowmik, Mithun
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2106.08794

openalex publication_date 2021/06/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We establish sharp Adams type inequalities on Sobolev spaces W^{α, n/α}(X) of any fractional order α< n on Riemannian symmetric space X of noncompact type with dimension n and of arbitrary rank. We also establish sharp Hardy-Adams inequalities on the Sobolev spaces W^{n/2, 2}(X). For the real hyperbolic spaces, such results were recently obtained by J. Li et al. (Trans. AMS, 2020). We use Fourier analysis on the symmetric spaces to obtain these results.

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