Affiliation:
1. Samarkand State University named after Sh. Rashidov
Abstract
Maximal operators associated with singular hypersurfaces in multidimensional Euclidean spaces are considered. We prove the boundedness of these operators and define a critical exponent in the space of summable functions, when hypersurfaces are given by parametric equations.
Reference14 articles.
1. Stein E.M. Maximal functions. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (7), 2174–2175 (1976).
2. Bourgain J. Averages in the plane convex curves and maximal operators, J. Anal. Math. 47, 69–85 (1986).
3. Greenleaf A. Principal curvature and harmonic analysis, Indiana Univ. Math. J. 30 (4), 519–537 (1981).
4. Sogge C.D. Maximal operators associated to hypersurfaces with one nonvanishing principal curvature, Fourier analysis and partial differential equations, Stud. Adv. Math, 317–323 (1995).
5. Sogge C.D., Stein E.M. Averages of functions over hypersurfaces in BbbR n, Invent. Math. 82 (3), 543–556 (1985).