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On the boundedness of maximal operators associated with singular surfaces

Salim E. Usmanov

Samarkand State University named after Sh. Rashidov, Samarkand, Uzbekistan

Abstract: The paper is devoted to investigate maximal operators associated with singular surfaces. It is proved the boundedness of these operators in the space $L^{p},$ when singular surfaces are given by parametric equations in $\mathbb{R}^{3}.$

Keywords: maximal operator, averaging operator, fractional power series, nonsingular point, critical exponent.

UDC: 517.9

Received: 10.03.2023
Received in revised form: 15.06.2023
Accepted: 14.03.2024

Language: English