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TICMI

## MATHEMATICS  AND  INFORMATICS

### ANNOUNCEMENTS FOR 2003

CALL FOR PAPERS

On April 22-24, 2003 the Enlarged Sessions of the Seminar of I. Vekua Institute of Applied Mathematics of I. Javakhishvili Tbilisi State University will be held under the support of ISMP at UNESCO.

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: March 1, 2003.

Registration fee is $200. The publishing of proceedings of the reports of the seminar is planned. The diskette of the report, not exceeding 4 printed pages, in English, using TEX, LATEX, AMSTEX, AMSLATEX programs, together with a hardcopy should be submitted to the organizers of the Seminar during the seminar days. The work of the seminar will start on April 22, 2003, at 10.00 at I. Vekua Institute of Applied Mathematics of I.Javakhishvili Tbilisi State University (2, University st.) Organizing Committee #### & & & #### Advanced Course on Function Spaces and Applications 2 Date: 13 - 20 September, 2003 Location: TICMI (Tbilisi) Vakhtang Kokilashvili (A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, Tbilisi, Georgia) INTEGRAL OPERATORS IN BANACH FUNCTION SPACES WITH VARIABLE EXPONENT Summary: The Banach function spaces with variable exponent and related Sobolev- type spaces proved to be an appropriate tool to study models with non-standard local growth (in elasticity theory, physics, fluid mechanics, differential equation). Those applications stimulate a quickly developing progress in the theory of mentioned spaces. Although the spaces$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, Academy of Scinces, Czech Republic)

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, University St. 2, Tbilisi 0143, Georgia

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

Tel.:+995 32 305995

#### Workshop "Polynomials and Their Applications"

Date: 22-24 September, 2003

Location: TICMI (Tbilisi)

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

Further information: TICMI, I.Vekua Institute of Applied Mathematics of Tbilisi State University, University St. 2, Tbilisi 0143, Georgia

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

Tel.:+995 32 305995

Vekua Institute of Applied Mathematics