  The characterization and construction of bent functions are challenging
problems. The paper generalizes the constructions of Boolean bent functions by
Mesnager \cite{M2014}, Xu et al. \cite{XCX2015} and $p$-ary bent functions by
Xu et al. \cite{XC2015} to the construction of $p$-ary weakly regular bent
functions and presents new infinite families of $p$-ary weakly regular bent
functions from some known weakly regular bent functions (square functions,
Kasami functions, and the Maiorana-McFarland class of bent functions). Further,
new infinite families of $p$-ary bent idempotents are obtained.
