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Sharp Adams Type Inequalities for the Fractional Laplace–Beltrami Operator on Noncompact Symmetric Spaces

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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 \(W^{n/2, 2}(X)\). We use Fourier analysis on the symmetric spaces to obtain these results.

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Acknowledgements

The author is supported by INSPIRE Faculty Award (IFA19-MA136) from Department of Science and Technology, India. The author is thankful to Swagato K Ray for numerous useful discussions and detailed comments. The author is also grateful to Sundaram Thangavelu and Rajesh K Singh for valuable suggestions for the improvement of the paper.

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  1. Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

    Mithun Bhowmik

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Bhowmik, M. Sharp Adams Type Inequalities for the Fractional Laplace–Beltrami Operator on Noncompact Symmetric Spaces. J Geom Anal 34, 211 (2024). https://doi.org/10.1007/s12220-024-01565-1

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