A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in Gauss space is offered. unified approach proposed, providing one with criteria their validity class rearrangement-invariant function norms. Optimal target and domain norms relevant are characterized via a reduction principle to one-dimensional Calderón type integral patterned on Gaussian isoperimetric f...

In this work we study the Lebesgue property for convex risk measures on the space of bounded càdlàg random processes (R∞). Lebesgue property has been defined for one period convex risk measures in [16] and earlier had been studied in [9] for coherent risk measures. We introduce and study the Lebesgue property for convex risk measures in the multi period framework. We give presentation of all co...

Let [Formula: see text], text] and be a singular or fractional integral operator with homogeneous kernel text]. In this paper, CMO type space is introduced studied. particular, the relationship between Lipchitz discussed. Moreover, necessary condition of restricted boundedness iterated commutator on weighted Lebesgue spaces via functions in an equivalent characterization compactness for are obt...

Abstract For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions with respect to into an almost dominated part singular part, analogous decomposition for measures in which case speaks absolutely continuous part. complete parametrization all will be given, uniqueness such characterized. In addition, it shown that has abstract Radon–Nikodym deri...

We give a complete characterization of integral functionals which are Lipschitzian on a Lebesgue space Lp with p finite. When the measure is atomless, we characterize the integral functionals which are locally Lipschitzian on such Lebesgue spaces Lp. In every cases, the Lipchitzian properties of the integral functional are described by Lipschitzian properties of the integrand. Mathematics Subje...