Maximal operators associated with singular surfaces

Sailm E. Usmanov^ab, Ismail Ekincioglu<sup>c

a</sup> Samarkand State University named after Sharof Rashidov, Samarkand, Uzbekistan
^b Kimyo International University in Tashkent, Tashkent, Uzbekistan
^c Istanbul Medeniyet University, Istanbul, Turkey

Abstract: Maximal operators associated with a class of singular parametrized surfaces in $\mathbb{R}^{3}$ are analyzed in the paper. Boundedness of such operators in Lebesgue $L^{p}$ space for $p>2$ is shown. It is also proved that at least one of the principal curvatures does not vanish at each regular point of these surfaces.

Keywords: Maximal operator, averaging operator, fractional power series, singular surface, principal curvatures.

UDC: 517.9

Received: 10.09.2024
Received in revised form: 27.11.2024
Accepted: 19.10.2025

Language: English