Bochner-Riesz means on a conical singular manifold

Abstract

We prove a sharp $L^p$-boundedness criterion for Bochner-Riesz multipliers on flat cones $X = (0,\infty) \times \mathbb{S}_\sigma^1$. The operator $S_\lambda^\delta(\Delta_X)$ is bounded on $L^p(X)$ for $1 \leq p \leq \infty$, $p \neq 2$, if and only if $\delta > \delta_c(p,2) = \max\left\{ 0, 2\left| 1/2 - 1/p \right| - 1/2 \right\}$. This result is also applicable to the infinite sector domain with Dirichlet or Neumann boundary, resolving the critical exponent problem in this wedge setting.