I. A. Ikromov, A. M. Barakayev, “On estimates for maximal operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, Number 7,Pages <nobr>23

On estimates for maximal operators

I. A. Ikromov^a, A. M. Barakayev^b

^a V. I. Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan, 15 University str., Samarkand, 140104 Republic of Uzbekistan
^b Samarkand state University, 15 University blvd., Samarkand, 140104 Republic of Uzbekistan

Abstract: The paper deals with boundedness problem for maximal operators associated to hypersurfaces in the space of integrable functions with degree p. A necessary condition for boundedness is given in the space of square-integrable functions in the case one nonvanishing principal curvature. A criterion for the boundedness of the maximal operators in the space of square-integrable functions is obtained for a partial class of convex hypersurfaces.

Keywords: maximal operator, Fourier transform, hypersurface, boundedness.

UDC: 517.518

Received: 29.03.2022
Revised: 19.04.2023
Accepted: 29.05.2023

DOI: 10.26907/0021-3446-2023-7-23-33