Abstract:
The study of differentiation of integrals has led to the study of maximal functions. In the development of harmonic analysis, the most powerful result connected with Lebesgue's theorem was that of the Hardy-Littlewood Maximal Theorem. This maximal theorem implies Lebesgue's theorem, and the maximal function and its variants have played an important role in many areas of harmonic analysis such as singular integral operators, Hardy spaces, BMO (bounded mean oscillation) spaces. One of the variants of the maximal function is the maximal function along hypersurfaces. In this dissertation, we will investigate the boundedness of the maximal function along surfaces of revolution in Euclidean spaces. Following the Calderon- Zygmund method of rotation, we shall further investigate its boundedness in Lebesgue mixed norm spaces.
