Jacek Dziubański

Hardy space

Let {Tt}t>0 be the semigroup of linear operators generated by a Schrodinger operator -A = ? - V, where V is a nonnegative potential that belongs to a certain reverse Holder class. We define a Hardy space HA1 by means of a maximal function associated with the semigroup {Tt}t>0. Atomic and Riesz transforms characterizations of HA1 are shown.

H^1

SummaryWe prove that densities of the measures in a strictly stable semigroup (ht) of symmetric measures on a homogeneous group, if they exist, have the following asymptotic behaviour:

Asymptotic behaviour of densities of stable semigroups of measures

\mathop {\lim |}\limits_{|x| \to \infty } x|^{Q + \alpha } \cdot h_1 (x) = k(\bar x),

Triebel-Lizorkin spaces associated with Laguerre and Hermite expansions

where α is the characteristic exponent,

Scattering of small solutions to generalized Benjamin-Bona-Mahony equation in several space dimensions

\bar x = |x|^{ - 1} x

On Riesz Transforms Characterization of H1 Spaces Associated with Some Schrödinger Operators

, andk is the density of the Lévy measure associated to the semigroup. Moreover, if