**CALL
FOR PAPERS**

On

The sections of the seminar are :

Partial differential equations (directed by Prof. George Jaiani, scientific secretary – Prof. Temur Jangveladze)

Mechanics of deformable solids (directed by Prof. Mikheil Basheleishvili, scientific secretary – Prof. Merab Svanadze).

At the Seminar 20-minute reports will be delivered.

Those wishing to participate are asked to contact by E-mail:

jaiani@viam.sci.tsu.ge

Deadline for applications:

Registration fee is $200.

The publishing of proceedings of the reports of the seminar is planned. The
diskette of the report, not exceeding 4 printed pages, in English, using

The work of the seminar will start on

Organizing
Committee

Date: 13 - 20 September, 2003

Location: TICMI (

**Vakhtang Kokilashvili** (A. Razmadze Mathematical Institute of the

INTEGRAL OPERATORS IN BANACH FUNCTION SPACES WITH VARIABLE EXPONENT

**Summary:** The Banach function spaces with variable exponent and
related Sobolev- type spaces proved to be an appropriate tool to study models
with non-standard local growth (in elasticity theory, physics, fluid mechanics,
differential equation). Those applications stimulate a quickly developing
progress in the theory of mentioned spaces.

Although the spaces $L^{p(\cdot)}$ posseses some undesirable properties (functions from these spaces are not $p(x)$-mean continuos, the space $L^{p(\cdot)}(\Omega)$ is not translation invariant, convolution operators in general do not behave well and so on).

In our lecture we plan to give the solutions of the boundedness and compactness problems in weighted Banach function spaces for classical integral operators. In particular, we will present the boundedness criteria for the Hilbert transform, Cauchy singular integrals and potentials in weighted Lebesgue spaces with power weights.

Some applications to singular integral equations and boundary value problems for analytic functions within the framework of the spaces with variable exponent will treated.

**Alois Kufner** (Mathematical Institute,

HARDY INEQUALITY AND ITS MODIFICATIONS

**Summary: **As a continuation of the lecture series presented at TICMI
1999, this time the series will deal with several problems connected with the
Hardy inequality and its modifications, in particular, with

- higher order inequalities for well-determined and overdetermined classes of functions,
- fractional order Hardy inequalities,
- weighted inequalities on cones of functions,
- the llimit case of Hardy’s inequality (i.e., the Carleman-Knopp inequality),
- the critical exponent for compact weighted imbeddings.

These results will be used to derive some (basic) properties of the spectra of some (in general nonlinear) degenerates and singular differential operators.

**Coordinator:** George Jaiani

This course is suitable for advanced graduate students or recent Ph.D.'s. The participants will also have an opportunity to give 20-minute talkes on their own work at a mini-symposium which will take place during the Advanced Course. Lectures and abstracts of the talks will be published and distributed among the lecturers and participants after Advanced Course. The registration fee for participants is 400 USD which includes all local expenses during the Advanced Course. A restricted number of participants will be awarded grants.

**Further information**: TICMI, I.Vekua Institute of Applied Mathematics
of Tbilisi State University,

e.mail: jaiani@viam.sci.tsu.ge

Tel.:+995 32 305995

Date: 22-24 September, 2003

Location: TICMI (

**Coordinators: **Prof. G. Jaiani,
Prof. P.E. Ricci

**Further information**: TICMI, I.Vekua Institute of Applied Mathematics
of Tbilisi State University,

e.mail: jaiani@viam.sci.tsu.ge

Tel.:+995 32 305995