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Bilinear Bochner-Riesz Means on the Complex Sphere
Abstract
In this paper, we establish the boundedness of the bilinear Bochner-Riesz means β¬Ξ±R on the complex sphere π. More precisely, we prove that β¬Ξ±R is bounded from Lp1(π) Γ Lp2(π) β Lp(π) where 1/p1+1/p2=1/p and 1β€ p1, p2 β€ β, for an admissible range of exponents, with the required smoothness parameter Ξ± described in terms of the topological dimension of π. To facilitate our proof, we establish several analytic estimates, including restriction-type estimates, weighted Plancherel estimates with large power of weights and bilinear weighted Plancherel estimates, which are derived from the ground up in our setting and may be considered of independent interest.
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BibTeX
@misc{bagchi2026bilinear,
title = {{Bilinear Bochner-Riesz Means on the Complex Sphere}},
author = {Sayan Bagchi and Md Nurul Molla and Joydwip Singh and Manasa N. Vempati},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.25884},
eprint = {2608.25884},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.25884},
}
RIS
TY - UNPB
TI - Bilinear Bochner-Riesz Means on the Complex Sphere
AU - Sayan Bagchi
AU - Md Nurul Molla
AU - Joydwip Singh
AU - Manasa N. Vempati
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.25884
UR - https://arxiv.org/abs/2608.25884
AB - In this paper, we establish the boundedness of the bilinear Bochner-Riesz means β¬^Ξ±_R on the complex sphere π. More precisely, we prove that β¬^Ξ±_R is bounded from L^p_1(π) Γ L^p_2(π) β L^p(π) where 1/p_1+1/p_2=1/p and 1β€ p_1, p_2 β€ β, for an admissible range of exponents, with the required smoothness parameter Ξ± described in terms of the topological dimension of π. To facilitate our proof, we establish several analytic estimates, including restriction-type estimates, weighted Plancherel estimates with large power of weights and bilinear weighted Plancherel estimates, which are derived from the ground up in our setting and may be considered of independent interest.
ER -