We continue the study on the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the cubic fourth order nonlinear Schrödinger equation. By considering the renormalized equation, we extend the quasi-invariance results in [29], [26] to Sobolev spaces of negative regularity. Our proof combines the approach introduced by Planchon, Tzvetkov, and Visciglia [34] with the normal form approach in [29], [26].

中文翻译：

---

负 Sobolev 空间中三次四阶非线性薛定谔方程的拟不变高斯测度

我们继续研究三次四阶非线性薛定谔方程动力学下Sobolev空间上高斯测度的输运性质。通过考虑重整化方程，我们将 [29]、[26] 中的准不变性结果扩展到负正则性的 Sobolev 空间。我们的证明将 Planchon、Tzvetkov 和 Visciglia [34] 引入的方法与 [29]、[26] 中的范式方法相结合。