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

We prove that the jump quasi-seminorm of order ϱ=2 for a general Ornstein--Uhlenbeck semigroup (H_t)t>0 in ℝn 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 (H_t)t>0, recently proved by the authors when ϱ>2, and disproved for ϱ=2.