  We analyse Morrey spaces, generalised Morrey spaces and Campanato spaces on
homogeneous groups. The boundedness of the Hardy-Littlewood maximal operator,
Bessel-Riesz operators, generalised Bessel-Riesz operators and generalised
fractional integral operators in generalised Morrey spaces on homogeneous
groups is shown. Moreover, we prove the boundedness of the modified version of
the generalised fractional integral operator and Olsen type inequalities in
Campanato spaces and generalised Morrey spaces on homogeneous groups,
respectively. Our results extend results known in the isotropic Euclidean
settings, however, some of them are new already in the standard Euclidean
cases.
