A Note on the [Formula omitted] Integrability of a Class of Bochner-Riesz Kernels

For a general compact variety [Formula omitted] of arbitrary codimension, one can consider the [Formula omitted] mapping properties of the Bochner-Riesz multiplier m[GAMMA],[alpha](ζ)=dist(ζ,[GAMMA])[alpha][phi](ζ)where [Formula omitted] and [Formula omitted] is an appropriate smooth cutoff function. Even for the sphere [Formula omitted], the exact [Formula omitted] boundedness range remains a central open problem in Euclidean harmonic analysis. In this paper we consider the [Formula omitted] integrability of the Bochner-Riesz convolution kernel for a particular class of varieties (of any codimension). For a subclass of these varieties the range of [Formula omitted] integrability of the kernels differs substantially from the [Formula omitted] boundedness range of the corresponding Bochner-Riesz multiplier operator.