PreprintCC BY 4.0arXiv
Bochner-Riesz means for Laguerre expansions
Abstract
We investigate the Lp norm convergence of Bochner-Riesz means SRδf, f ∈ Lp(ℝ+,dμβ) associated to Laguerre expansions of type β≥ −1/2. For any given 1 < p < ∞ and β> −1/2, we provide a complete characterisation of the order δ for which these means are uniformly bounded on Lp spaces. A particularly noteworthy phenomenon arises for −1/3 <β<0, where the admissible $(p, δ)$ region differs substantially from those for $ -1/2 \leq β\leq -1/3$ or β≥ 0. Interestingly, the convergence for −1/3 < β<0 is an interaction between the ranges $ -1/2 \leq β\leq -1/3$ and β≥ 0.
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BibTeX
@misc{sharma2026bochnerriesz,
title = {{Bochner-Riesz means for Laguerre expansions}},
author = {Himani Sharma and Adam Sikora and Sundaram Thangavelu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01221},
eprint = {2611.01221},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01221},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bochner-Riesz means for Laguerre expansions
AU - Himani Sharma
AU - Adam Sikora
AU - Sundaram Thangavelu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01221
UR - https://arxiv.org/abs/2611.01221
AB - We investigate the L^p norm convergence of Bochner-Riesz means S_R^δf, f ∈ L^p(ℝ^+,dμ_β) associated to Laguerre expansions of type β≥ −1/2. For any given 1 < p < ∞ and β> −1/2, we provide a complete characterisation of the order δ for which these means are uniformly bounded on L^p spaces. A particularly noteworthy phenomenon arises for −1/3 <β<0, where the admissible $(p, δ)$ region differs substantially from those for $ -1/2 \leq β\leq -1/3$ or β≥ 0. Interestingly, the convergence for −1/3 < β<0 is an interaction between the ranges $ -1/2 \leq β\leq -1/3$ and β≥ 0.
ER -