Bochner-Riesz commutators for Grushin Operators

2025/05/22 by Md Nurul Molla, Molla, Md Nurul, Joydwip Singh +1
Mathematics · #42B15 #43A85 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Approximation Theory and Sequence Spaces #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2505.16593

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the boundedness of Bochner-Riesz commutator [b, S^α(L)](f) = b S^α(L)(f) - S^α(L)(bf) of a BMO^\varrho(ℝ^d) function b and the Bochner-Riesz operator S^α(L) associated to the Grushin operator L on ℝ^d with d:= d₁ +d₂. We prove that for 1≤ p ≤ min \2d₁/(d₁ +2), 2(d₂ +1)/(d₂+3)\ and α> d(1/p - 1/2) - 1/2, if b ∈ BMO^\varrho(ℝ^d), then [b, S^α(L)] is bounded on L^q(ℝ^d) whenever p < q < p'. Moreover, if b ∈ CMO^\varrho(ℝ^d), then we show that [b, S^α(L)] is a compact operator on L^q(ℝ^d) in the same range.

Citations

• The commutators of Bochner-Riesz Operators for Hermite operator
• Lie group approach to Grushin operators
• Spectral multipliers of self-adjoint operators on Besov and Triebel--Lizorkin spaces associated to operators
• Compactness of Riesz transform commutator associated with Bessel operators
• Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means
• Riesz transforms and multipliers for the Grushin operator

Related

• The commutators of Bochner-Riesz Operators for Hermite operator
• Bilinear Bochner-Riesz Means for Grushin Operators
• L^p-boundedness of the Bochner-Riesz operator
• Riesz transforms and multipliers for the Grushin operator
• A proof of the Bochner-Riesz conjecture