  This paper gives a short survey of some basic results related to estimates of
fractional integrals and Fourier transforms. It is closely adjoint to our
previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in
the paper are based on nonincreasing rearrangements. We give alternative proofs
of some results.
  We observe also that the paper represents the mini-course given by the author
at Barcelona University in October, 2014.
