Let be the homogenous vector bundle over associated to an irreducible representation of Sp(1). We give an image characterization of the Poisson transform of -section of . We also show that , satisfies a Hardy-type estimate.
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Achraf Ouald Chaib 1

@article{CRMATH_2024__362_G3_265_0, author = {Achraf Ouald Chaib}, title = {On the {Poisson} transform on a homogenous vector bundle over the quaternionic hyperbolic space}, journal = {Comptes Rendus. Math\'ematique}, pages = {265--273}, publisher = {Acad\'emie des sciences, Paris}, volume = {362}, year = {2024}, doi = {10.5802/crmath.550}, language = {en}, }
TY - JOUR AU - Achraf Ouald Chaib TI - On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space JO - Comptes Rendus. Mathématique PY - 2024 SP - 265 EP - 273 VL - 362 PB - Académie des sciences, Paris DO - 10.5802/crmath.550 LA - en ID - CRMATH_2024__362_G3_265_0 ER -
Achraf Ouald Chaib. On the Poisson transform on a homogenous vector bundle over the quaternionic hyperbolic space. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 265-273. doi : 10.5802/crmath.550. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.550/
[1] Hardy-type spaces for eigenfunctions of invariant differential operators on homogeneous line bundles over Hermitian symmetric spaces, Complex Variables, Theory Appl., Volume 48 (2003) no. 10, pp. 865-876 | DOI | MR | Zbl
[2] On Poisson transforms for differential forms on real hyperbolic spaces (2021) | arXiv
[3] On Poisson transform for spinors, Tunis. J. Math., Volume 5 (2023) no. 4, pp. 771-792 | DOI | MR
[4] Fatou’s theorems and Hardy-type spaces for eigenfunctions of the invariant differential operators on symmetric spaces, Int. Math. Res. Not. (2003) no. 16, pp. 915-931 | DOI | MR | Zbl
[5] -Poisson integral representations of eigensections of invariant differential operators on a homogeneous line bundle over the complex Grassmann manifold , Ann. Global Anal. Geom., Volume 61 (2022) no. 2, pp. 399-426 | DOI | MR | Zbl
[6] A characterization of the -range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces, J. Geom. Phys., Volume 194 (2023), 105019 | DOI | MR
[7] Characterization of the -range of the Poisson transform in Hyperbolic spaces, J. Lie Theory, Volume 12 (2002) no. 1, pp. 1-14 | MR | Zbl
[8] On the Poisson transform on symmetric spaces of real rank one, J. Funct. Anal., Volume 174 (2000) no. 2, pp. 513-523 | DOI | MR | Zbl
[9] A characterization of the -range of the Poisson transform related to Strichartz conjecture on symmetric spaces of noncompact type, Adv. Math., Volume 303 (2016), pp. 464-501 | DOI | MR | Zbl
[10] Eigenfunctions of invariant differential operators on a symmetric space, Ann. Math., Volume 107 (1978), pp. 1-39 | DOI | MR | Zbl
[11] Characterization of almost -eigenfunctions of the Laplace–Beltrami operator, Trans. Am. Math. Soc., Volume 366 (2014) no. 6, pp. 3191-3225 | DOI | MR | Zbl
[12] Die Poisson-transformation für homogene Vektorbündel, Ph. D. Thesis, Humboldt-Unversität, Berlin, Germany (1995)
[13] Vector valued Poisson transforms on Riemannian symmetric spaces of rank one, J. Funct. Anal., Volume 119 (1994) no. 2, pp. 358-400 | DOI | MR | Zbl
[14] Poisson transforms on vector bundles, Trans. Am. Math. Soc., Volume 350 (1998) no. 3, pp. 857-887 | DOI | MR | Zbl
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