A family of Bochner–Riesz type multipliers on the two-dimensional disk

Let s=(ν,μ)∈R2 and define on R2. Given p∈[1,+∞[, we prove some necessary and sufficient conditions on s such that ms be a Fourier multiplier for Lp. We employ two different techniques, according to ν=0 or ν≠0. In the latter case, the results obtained are optimal.