  We study the mapping properties of fractional maximal operators in Sobolev
and Campanato spaces in metric measure spaces. We show that, under certain
restrictions on the underlying metric measure space, fractional maximal
operators improve the Sobolev regularity of functions and map functions in
Campanato spaces to H\"older continuous functions. We also give an example of a
space where fractional maximal function of a Lipschitz function fails to be
continuous.
