In non-isotropic riesz potentials differantiability

IN NON-ISOTROPIC RIESZ POTENTIALS DIFFERANTIABILITY ( M.Sc. Thesis ) Derya KÖKER ( ÇAVUŞ ) GAZİ UNIVERSITY INSTITUTE OF SCIENCE AND TECHNOLOGY August 1999 ABSTRACT In this study, the definition of Riesz potentials is given and after that some main especialities are given. This thesis is consist of four parts. In the first part which is the introduction part,it was given the historical developments of Riesz potential and different properties of it. After that it was given that the definition of Riesz potential according to the non- isotropic kernel. In the second part, it was given some necessary properties to be differentiated. In the third part, Riesz potentials' differentiability were shown.. The fourth part is original. In this part it was given some necessary properties of X - Riesz potentials according to the non-isotropic kernel. Science Code : Key words : Potential, Riesz potential, Totally differentiability, Weak singularity, Kernel of an integral operator. Page Number : 52 Adviser : Assoc.Prof.Dr. Esin İnan ÇINAR