Weak type (1,1) jump inequalities in a nonsymmetric Gaussian setting

Journal article, 2026

We prove that the jump quasi-seminorm of order ϱ = 2 for a general Ornstein–Uhlenbeck semigroup (Ht)_t>0 in R^n defines an operator of weak type (1, 1) with respect to the invariant measure. This provides an example of a weak-type jump inequality for a nonsymmetric semigroup in a nondoubling measure space. Our result may be seen as an endpoint refinement of the weak type (1, 1) inequality for the ϱ-th order variation seminorm of (Ht)_t>0, recently proved by the authors when ϱ > 2, and disproved for ϱ = 2