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.
stand 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,. . .