Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality

Extremal Spaces Related to Schrödinger Operators with Potentials Satisfying a Reverse Hölder Inequality

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 ...

Localized 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...

Ground State for the Schrödinger Operator with the Weighted Hardy Potential

A Reverse Hardy-hilbert-type Integral Inequality

By estimating a weight function, a reverse Hardy-Hilbert-type integral inequality with a best constant factor is obtained. As an application, some equivalent forms and some particular results have been established.

Orlicz-Hardy Spaces Associated with Operators Satisfying Davies-Gaffney Estimates

Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The ...