  We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato,
Lipschitz, $B^p$, CMO, local Morrey-type spaces, etc., and investigate the
interpolation property of $B_w^u$-function spaces. We also apply it to the
boundedness of linear and sublinear operators, for example, the
Hardy-Littlewood maximal and fractional maximal operators, singular and
fractional integral operators with rough kernel, the Littlewood-Paley operator,
Marcinkiewicz operator, and so on.
