ABSTRACT
V. KOKILASHVILI, A. MESKHI A. Razmadze Mathematical Institute of the Georgian Academy of Sciences
INTRODUCTION
In this lecture we present a survey of authors’ recent results concerning with two-weight problems for fractional integral transforms and singular integrals. Most of these results were obtained after appearing of the monograph [1] including the contemporary investiga tions in the weight theory of integral transforms (potentials, maximal functions, fractional and singular integrals) defined on the general structures, i.e. so called Spaces of Homo geneous Type. The results presented in this survey solve the open problems which arised in [1]. For the previous surveys and books dealing with the weight problems we refer to [2-10]. Some applications of two-weight estimates were illustrated in [ 11 -12].
