Riesz potential in generalized grand Lebesgue spaces

Jan 2017
I would like to draw your attention to the mathematical research in the fields of functional spaces and operator theory, which is carried out at Academy of Sciences of Chechen Republic in cooperation with University of Algarve and Southern Federal University. The paper is in Russian, so if there is any problem with translating I will be glad to help.

The Riesz potentials play a significant role in mathematical physics, potential theory, fractional calculus and other areas of modern Mathematics. The generalized grand Lebesgue spaces are currently of a great interest for professional mathematicians as they are essential for developing the concept of integrability. The present paper provides conditions for the Riesz potential operator to be bounded in the generalized grand Lebesgue spaces over the real coordinate space of n dimensions.

Research Paper: "Riesz potential in generalized grand Lebesgue spaces"​