Bochner-Riesz means associated with conical surfaces

Let d1 and d2 be two nonnegative integers greater than 2. We study the Fourier multiplier Tλ associated with a conical surface S={(ξ,τ)∈Rd1×Rd2:|ξ|=|τ|}, defined by Tλf̂(ξ,τ)=(1−|ξ|2|τ|2)+λΨ(|τ|)f̂(ξ,τ),(ξ,τ)∈Rd1×Rd2, where Ψ is a smooth function defined on R, that is supported in (1/2,2).