Bochner-Riesz means on a conical singular manifold

Abstract

We prove a sharp $L^p$-boundedness criterion for Bochner-Riesz multipliers on flat cones $X=(0,\infty )\times {\mathbb{S}}_{\ddot{I}}{ƒ}^1$. The operator $S_{\hat{I}}{»}^{\hat{I}}´(\hat{I}{”}_X)$ is bounded on $L^p(X)$ for $1\le p\le \infty$, $p\ne 2$, if and only if $\hat{I}´>\hat{I}{´}_c(p,2)=\max \left\{0,2\left|1/2-1/p\right|-1/2\right\}$. This result is also applicable to the infinite sector domain with Dirichlet or Neumann boundary, resolving the critical exponent problem in this wedge setting.

33 pages, Comments are welcome!