Connections between quaternary and Boolean bent functions

This work is related to quaternary bent functions $f:\mathbb{Z}_4^n\rightarrow\mathbb{Z}_4$. The relation between Walsh — Hadamard transform coefficients of quaternary and two Boolean functions is explored. It is proved that any quaternary bent function is a regular bent function for any $n$. The number of quaternary bent functions in one and two variables is counted. For quaternary bent function in one variable $g(x+2y)=a(x,y)+2b(x,y)$, it is proved that $b$ and $a\oplus b$ are Boolean bent functions, where $x,y\in\mathbb{Z}_2$. Properties of Boolean functions $a,b$ and $a\oplus b$ in representation of quaternary bent function in two variables as $g(x+2y)=a(x,y)+2b(x,y)$ are described.