Singular Integrals with Respect to the Gaussian Measure

Riesz transforms on variable Lebesgue spaces with Gaussian measure

“…with continuous first-order derivatives) that is orthogonal to γ , that is, R n F(z)e −|z| 2 dz = 0. These type of operators were first introduced by Urbina [9] (see also [13]).…”

“…In order to do so, we will allow the function F to have some exponential growth (see [9,13]). That is, let us assume that F satisfies that for every > 0 there exists a positive constant C such that…”

“…Later, Meyer [6] and Gundy [7] gave probabilistic proofs for any order and dimension. From the analytical point of view, and using several and different techniques, we can cite, chronologically, the works of Pisier [8], Urbina [9], Gutiérrez [10], Gutiérrez et al [11], Forzani et al [12], and Pérez [13]. Other works that include this boundedness are [14,15].…”

Riesz transforms of a general Ornstein–Uhlenbeck semigroup

“…In the standard case, when Q and −B are the identity matrix, the strong type (p, p) of R ( ) has been proved with different techniques in [10,13,16,22,24,29,31]; for a recent account of this case we refer to [32,Chapter 9]. Other proofs, holding in the more general case Q = I and B symmetric, may be found in [17,18].…”