Extremal Spaces Related to Schrödinger Operators with Potentials Satisfying a Reverse Hölder Inequality
نویسندگان
چکیده
We describe some elements of the theory of semigroups generated by second order differential operators needed to study the Hardy-type space H1 L related to the time independent Schrödinger operator L = −∆+ V , with V ≥ 0 a potential satisfying a reverse Hölder inequality. Its dual space is a BMO-type space BMOL, that turns out to be the suitable one for the versions of some classical operators associated to L (Hardy-Littlewood, semigroup and Poisson maximal functions, square function, fractional integral operator). We also recall a characterization of BMOL in terms of Carlesson measures.
منابع مشابه
Regularity in Orlicz spaces for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition∗
The purpose of this paper is to obtain the global regularity in Orlicz spaces for nondivergence elliptic operators with potentials satisfying a reverse Hölder condition.
متن کاملLocalized Hardy Spaces H Related to Admissible Functions on RD-Spaces and Applications to Schrödinger Operators
Let X be an RD-space, which means that X is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X . In this paper, the authors first introduce the notion of admissible functions ρ and then develop a theory of localized Hardy spaces H ρ (X ) associated with ρ, which includes several maximal function characterizations...
متن کاملL Boundedness of Riesz transform related to Schrödinger operators on a manifold
We establish various Lp estimates for the Schrödinger operator −∆ + V on Riemannian manifolds satisfying the doubling property and a Poincaré inequality, where ∆ is the Laplace-Beltrami operator and V belongs to a reverse Hölder class. At the end of this paper we apply our result on Lie groups with polynomial growth.
متن کاملExtension of Hardy Inequality on Weighted Sequence Spaces
Let and be a sequence with non-negative entries. If , denote by the infimum of those satisfying the following inequality: whenever . The purpose of this paper is to give an upper bound for the norm of operator T on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). We considered this problem for certain matrix operators such as Norlund, Weighted mean, Ceasaro and Copson ma...
متن کاملBoundedness for Riesz transform associated with Schrödinger operators and its commutator on weighted Morrey spaces related to certain nonnegative potentials
*Correspondence: [email protected] School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China Abstract Let L = – + V be a Schrödinger operator, where is the Laplacian on Rn and the nonnegative potential V belongs to the reverse Hölder class Bq for q≥ n/2. The Riesz transform associated with the operator L is denoted by T =∇(– + V)– 2 and the dual Ri...
متن کامل