On May 27-June 3, 2014 the leading research associate of the “Mathematical Analysis” department of IMM philosophy doctor on mathematics Rovshan Bandaliyev has participated in the International Conference “Fourier series and its application” held in Novorossiysk city of Russia. He has given a report “On boundedness of certain sublinear operator in weighted variable Lebesgue spaces”.
The importance of the Hardy inequality in classic harmonic analysis is known well. It is connected with generalization of this inequality in different weighted spaces including to certain Borel measures. Recent years the generalization of this inequality to rather abstract Banach functional spaces, ideal spaces and other spaces is of great interest.
Lately, consideration of the Hardy operator in variable degree Lebesgue spaces has also gained a great interest.
In this report the boundedness theorem in variable degree and weighted Lebesgue space was proved for a class of sublinear operators containing important integral operators of harmonic analysis. The Riesz potential, fractional-maximal operator, Fefferman’s singular integral, Carleson’s maximum operator, Bohner-Riesz averaging operator are among these mentioned operators.
The well known scientist of Russia prof. S.G.Samko, prof. M.L. Goldman, prof. B.I.Golubov also were among the participants. They have noted the use of this Conference from scientific point of view.