Restricted weak type endpoint estimate for the spherical maximal operators on the Heisenberg group

2025/02/28 by Jeon, Hyunwoo, Kim, Joonil
#42B15 #42B30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.20932

Abstract

Let ℍⁿ denote the Heisenberg group, identified with ℝ^d × ℝ, where d = 2n and n ∈ ℕ. We consider the spherical maximal operator M associated with the sphere S^d-1 embedded in the horizontal subspace ℝ^d × \0\ of ℍⁿ. It is known that M is bounded on L^p(ℍⁿ) if and only if p ∈ (\tfracdd-1, ∞]. In this paper, we establish a restricted weak type (p,p) estimate at the endpoint p = \tfracdd-1 for M, provided d ≥ 3.

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