Crescents and the Real Variable Cesàro Operator

Abstract This paper explores a version of the classical Cesàro integral operator for the Lebesgue space $$L^p(0, 1)$$ L p ( 0 , 1 ) where we discuss its norm, spectral properties, cyclicity, and invariant subspaces. The spectrum of the Cesàro operator will be a crescent domain whose geometry depends on p . An important tool will be semigroups of weighted composition operators on $$L^p(0, 1)$$ L p ( 0 , 1 ) .