Jacek Zienkiewicz

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

A simple proof of concentration of mass equal to

associated to Schrödinger operator with potential satisfying reverse Hölder inequality

8\pi

Optimal criteria for blowup of radial and N-symmetric solutions of chemotaxis systems

for blowing up

Precise tail asymptotics of fixed points of the smoothing transform with general weights

N

Large deviations for solutions to stochastic recurrence equations under Kesten’s condition

-symmetric solutions of the Keller--Segel model of chemotaxis in two dimensions with large

Large deviation estimates for exceedance times of perpetuity sequences and their dual processes

N

Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data

is given. Moreover, a criterion for blowup of solutions in terms of the radial initial concentrations, related to suitable Morrey spaces norms, is derived for radial solutions of chemotaxis in several dimensions. This condition is, in a sense, complementary to the one guaranteeing the global-in-time existence of solutions.

Atomic characterization of the Hardy space ¹_(ℝ) of one-dimensional Schrödinger operators with nonnegative potentials

We consider solutions of the stochastic equation

Convergence to Stable Laws for Multidimensional Stochastic Recursions: The Case of Regular Matrices

R=_d\sum_{i=1}^NA_iR_i+B