The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator Gauss space are detected. existence extremal functions relevant is also established. Our results disclose analogies and dissimilarities comparison with Adams' inequality Laplace operator, companion our Euclidean space.

<abstract><p>We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace inequalities. In order to get latter, we study solutions of associated extension problem. second develops a non-local version ground state representation in spirit Frank, Lieb, and Seiringer.</p></abstract>

In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.

Energy inequalities are derived for an elliptic-hyperbolic operator arising in plasma physics. These inequalities imply the existence of distribution and weak solutions to various closed boundary-value problems. An existence theorem is proven for a related class of Keldysh equations, and the failure of expected methods for obtaining uniqueness is discussed. The proofs use ideas recently introdu...

The present paper is about Bernstein-type estimates for Jacobi polynomials and their applications to various branches in mathematics. This is an old topic but we want to add a new wrinkle by establishing some intriguing connections with dispersive estimates for a certain class of Schrödinger equations whose Hamiltonian is given by the generalized Laguerre operator. More precisely, we show that ...