Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications
Abstract
Let λ>−1/2,≠0. Consider the Bessel operators Δλ:=−d2/dx2−2λ/xd/dx on ℝ+. In this paper, we first establish several characterizations for Ã∞,λ weights introduced by Li et al. (Math. Z. 309(1) (2025), Paper No. 13, 29pp), which are different from the previous Ap class with respect to the measure x2λdx. Among these characterizations, we obtain the sharp reverse Hölder inequality (RHI) for Ã∞,λ weights. As applications of RHI, we derive a precise open property of Ãp,λ weights, and obtain a sharp weighted bounds for the Hardy-Littlewood maximal operator ℳλ associated to Δλ, which was missing in the previous papers. Next, we also establish several extrapolation theorems related to Ãp,λ weights. Furthermore, we characterize the restricted weighted weak type estimates for ℳλ via a new class of weights Ãp,λℛ, which is strictly larger than Ãp,λ. Meanwhile, we obtain quantitative restricted weighted weak type (p,p) bounds for sparse operators. As applications, we derive various kinds of weighted inequalities for Riesz transforms, maximal operators, square functions, variation operators and their commutators associated to Δλ.
Related
- Local Matrix Muckenhoupt Weights and Quantitative Weighted Inequalities Achieving Global Best Known Exponents
- Properties and applications of Muckenhoupt A1 growth weights
- Pseudo-Differential and Fractional Schrödinger Operators on Grand Variable Herz–Morrey–Hardy Spaces with Muckenhoupt Weights
- Compact linear combination of composition operators on weighted Bergman-Orlicz spaces induced by doubling weights
- Muckenhoupt weights for the Hardy-Littlewood maximal operator on hyperbolic spaces
BibTeX
@misc{wen2026weighted,
title = {{Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications}},
author = {Yongming Wen and Huoxiong Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15260},
eprint = {2610.15260},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15260},
}
RIS
TY - UNPB
TI - Weighted norm inequalities for operators with new Muckenhoupt type weights in the Bessel setting and applications
AU - Yongming Wen
AU - Huoxiong Wu
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15260
UR - https://arxiv.org/abs/2610.15260
AB - Let λ>−1/2,≠0. Consider the Bessel operators Δ_λ:=−d^2/dx^2−2λ/xd/dx on ℝ_+. In this paper, we first establish several characterizations for Ã_∞,λ weights introduced by Li et al. (Math. Z. 309(1) (2025), Paper No. 13, 29pp), which are different from the previous A_p class with respect to the measure x^2λdx. Among these characterizations, we obtain the sharp reverse Hölder inequality (RHI) for Ã_∞,λ weights. As applications of RHI, we derive a precise open property of Ã_p,λ weights, and obtain a sharp weighted bounds for the Hardy-Littlewood maximal operator ℳ_λ associated to Δ_λ, which was missing in the previous papers. Next, we also establish several extrapolation theorems related to Ã_p,λ weights. Furthermore, we characterize the restricted weighted weak type estimates for ℳ_λ via a new class of weights Ã_p,λ^ℛ, which is strictly larger than Ã_p,λ. Meanwhile, we obtain quantitative restricted weighted weak type (p,p) bounds for sparse operators. As applications, we derive various kinds of weighted inequalities for Riesz transforms, maximal operators, square functions, variation operators and their commutators associated to Δ_λ.
ER -