Convergence in variation of the joint laws of multiple stable stochastic integrals

In this note, we are interested in the regularity in the sense of total variation of the joint laws of multiple stable stochastic integrals. Namely, we show that the convergence [formula] holds true as long as each kernel finconverges when n→+∞to fi in the Lorentz-type space [formula]. This result generalizes [4] from the one-dimensional case to the joint law case. It generalizes also [6] from the Wiener–Itô setting to the stable setting and [5] in the study of joint law of multiple stable integrals.