Abstract
On
we consider the Schrödinger operator
where
and
is a positive function (“potential”).
Let be the heat semigroup
associated with to .
In the talk we shall consider the Hardy space
which is a natural substitute of in
harmonic analysis associated with .
Our main interest will be in showing that elements
have decompositions
of the type ,
where
and
(“atoms”) have some nice properties.
In the classical case
on an atom is a
function for which
there exist a ball
such that
We shall see that for
we can still prove some atomic decompositions, but the
properties of atoms depend on the dimension d and the potential
.