The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on $L^2(\T)$ with covariance $[1+(-\D)^{ s}]^{ -1}$ under these transformations for any $s>\frac12$. This extends previous achievements by Nahmod, Ray-Bellet, Sheffield and Staffilani (2011) and Genovese, Luc\`a and Valeri (2018), who proved the result for integer values of the regularity parameter $s$.
Categories: math.PR math.AP math.FA