On 11.03.2016, at 12:00 the seminar of “Mathematical Analysis” department “Contemporary problems and applications of harmonic analysis” doc. lead. r. a. Elman Ibrahimov will deliver a lecture “Maximal function and Riesz potential generated by Gegenbauer differential operator”. In this report consider maximal functions generated by Gegenbauer differential operator and proved its Lp – boundedness. Introduce a Riesz-Gegenbauer potential and given its integral representation. Sobolev type theorem for Riesz-Gegenbauer potential is proved.