# $$L^p$$ L p Joint Eigenfunction Bounds on Quaternionic Spheres

$$L^p$$ L p Joint Eigenfunction Bounds on Quaternionic Spheres 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Fourier Analysis and Applications Springer Journals

# $$L^p$$ L p Joint Eigenfunction Bounds on Quaternionic Spheres

, Volume 23 (4) – Oct 14, 2016
33 pages

/lp/springer_journal/l-p-l-p-joint-eigenfunction-bounds-on-quaternionic-spheres-840u78XfUi
Publisher
Springer US
Subject
Mathematics; Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics
ISSN
1069-5869
eISSN
1531-5851
D.O.I.
10.1007/s00041-016-9506-6
Publisher site
See Article on Publisher Site

### Abstract

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

Journal of Fourier Analysis and ApplicationsSpringer Journals

Published: Oct 14, 2016

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