ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 42, 43, 44 Kokilashvili, Vakhtang, A. Razmadze Mathematical Institute, Georgia Solutions of Two-Weight Problems on Boundedness and Compactness for Integral Transforms The aim of the report is to present our results concerning the following problems: The necessary and sufficient conditions for a pair of weight functions insuring boundedness and compactness of integral transforms (involving potentials) defined on homogeneous type spaces (SHT). We do not use the notation of capacity; Criteria are given for the existence of bounded and compact imbeddings of Sobolev (Liouville) spaces into the Lebesgue space, generally speaking, with the different weights; Two-weight problems for singular integrals defined on SHT and multipliers of Fourier transform; Applications to PDE.