The work presented here is centered around the study of some of the real variable methods newly developed in a natural way for the treatment of different problems in Fourier Analysis, particularly for problems related to the pointwise convergence of some important operators. The key to understand these questions is the corresponding maximal operator and so the methods presented here concern the general Stein-Ni kishin theory, the general and special techniques that can be used to deal with different types of operators, the covering methods originated in differentiation 'theory, methods connected with the theory of singular integral operators, Fourier multipliers.

 

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