  In this paper, some topics of monotone operator theory in the setting of
Hadamard spaces are investigated. For a fixed element $p$ in a Hadamard space
$X$, the notion of $p$-Fenchel conjugate is introduced and a type of the
Fenchel-Young inequality is proved. Moreover, we examine the $p$-Fitzpatrick
transform and its main properties for monotone set-valued operators in Hadamard
spaces. Furthermore, some relations between maximal monotone operators and
certain classes of proper, convex, l.s.c. extended real-valued functions on
$X\times X^{\scalebox{0.7}{$^{\lozenge}$}}$, are given.
