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

Mithun Bhowmik

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arXiv · 2106.08794

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

Mithun Bhowmik

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Abstract

We establish sharp Adams type inequalities on Sobolev spaces $W^{\alpha, n/\alpha}(X)$ of any fractional order $\alpha< n$ 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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BibTeX RIS

Mithun Bhowmik. 2021-06-16. Sharp Adams type inequalities for the fractional Laplace-Beltrami operator on noncompact symmetric spaces. https://arxiv.org/abs/2106.08794

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