Lacunary δ-Discretised Spherical Maximal Operators

2025/07/14 by Choudhary, Surjeet Singh, Li, Ji, Liang, Chong-Wei +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.09962

Abstract

We study the lacunary analogue of the δ-discretised spherical maximal operators introduced by Hickman and Jančar, for δ∈ (0, 1/2), and establish the boundedness on L^p for all 1 < p < ∞, along with the endpoint weak-type estimate H¹ → L^1,∞. We also prove the corresponding L^p boundedness for the multi-parameter variant. The constants in these bounds are uniform in δ, and thus, by taking the limit δ→ 0⁺, our results recover the classical boundedness of the lacunary spherical maximal function.

Citations

• Improved L^p bounds for the strong spherical maximal operator
• Spherical maximal estimates via geometry
• L^p bound on the strong spherical maximal function
• A multi-parameter cinematic curvature
• The elliptic maximal function
• Lacunary maximal functions on homogeneous groups
• Nikodym sets and maximal functions associated with spheres
• On the Korányi Spherical maximal function on Heisenberg groups
• On the lacunary spherical maximal function on the Heisenberg group
• Lacunary spherical means
• Hp spaces of several variables

Related

• Lacunary spherical maximal operators on hyperbolic spaces
• Lacunary Discrete Spherical Maximal Functions
• Bounds for lacunary bilinear spherical and triangle maximal functions
• Spherical maximal estimates via geometry
• Improved L^p bounds for the strong spherical maximal operator