Optimal Sobolev embeddings for the Ornstein-Uhlenbeck operator

Logo poskytovatele

Varování

Publikace nespadá pod Filozofickou fakultu, ale pod Fakultu informatiky. Oficiální stránka publikace je na webu muni.cz.
Autoři

CIANCHI Andrea MUSIL Vít PICK Luboš

Rok publikování 2023
Druh Článek v odborném periodiku
Časopis / Zdroj Journal of Differential Equations
Fakulta / Pracoviště MU

Fakulta informatiky

Citace
www https://www.sciencedirect.com/science/article/pii/S0022039623001110
Doi http://dx.doi.org/10.1016/j.jde.2023.02.035
Klíčová slova Ornstein-Uhlenbeck operator; Gauss space; embeddings; optimality
Přiložené soubory
Popis A comprehensive analysis of Sobolev-type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space is offered. A unified approach is proposed, providing one with criteria for their validity in the class of rearrangement-invariant function norms. Optimal target and domain norms in the relevant inequalities are characterized via a reduction principle to one-dimensional inequalities for a Calderon type integral operator patterned on the Gaussian isoperimetric function. Consequently, the best possible norms in a variety of spe- cific families of spaces, including Lebesgue, Lorentz, Lorentz-Zygmund, Orlicz and Marcinkiewicz spaces, are detected. The reduction principle hinges on a preliminary discussion of the existence and uniqueness of generalized solutions to equations, in the Gauss space, for the Ornstein-Uhlenbeck operator, with a just integrable right-hand side. A decisive role is also played by a pointwise estimate, in rearrangement form, for these solutions.
Související projekty:

Používáte starou verzi internetového prohlížeče. Doporučujeme aktualizovat Váš prohlížeč na nejnovější verzi.