Regularity propertiesof maximal operators

In introduction section of this study, as to whether problem of possibleness to have continuity from boundness of nonlinear operators is discussed In abstract of bibliography section, summary of articles which close related with the dissertation topic were given. In material and method section, real analysis, functional analysis topics and some function spaces which make available to understanding the dissertaion were given. In findings and discussion section, continuity of maksimal operator, fixed points such as 𝑀(𝑓) = 𝑓 in 𝐿 𝑝 space and finally, we investigate the action of the maximal operator on Lipschitz and Hölder functions in the context of homogeneous spaces. Keywords: Maximal operator, Sublinear operator, Function spaces