Bochner–Riesz means for the twisted Laplacian in R²

We study the Bochner–Riesz problem for the twisted Laplacian L on R². For p ∊ [1; ∝] \ {2}, it has been conjectured that the Bochner–Riesz means S_λ^δ (L)f of order ı converge in L^p for every f ∊ L^p if and only if ı > max(0; j(p – 2)/pj – 1/2). We prove the conjecture by obtaining uniform L^p bounds on S_λ^δ (L) up to the sharp summability indices.