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We prove some sharp $$L^p-L^2$$ L p - L 2 estimates for joint spectral projections $$\pi _{\ell \ell '}$$ π ℓ ℓ ′ , with $$\ell ,\ell '\in {\mathbb {N}}$$ ℓ , ℓ ′ ∈ N , $$\ell \ge \ell '\ge 0$$ ℓ ≥ ℓ ′ ≥ 0 , $$1\le p\le 2$$ 1 ≤ p ≤ 2 , associated to the Laplace–Beltrami operator and to a suitably defined subLaplacian on the unit quaternionic sphere.
Journal of Fourier Analysis and Applications – Springer Journals
Published: Oct 14, 2016
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