  In this paper we establish the $L^p$-$L^q$ estimates for global
pseudo-differential operators on graded Lie groups. We provide both necessary
and sufficient conditions for the $L^p$-$L^q$ boundedness of
pseudo-differential operators associated with the global H\"ormander symbol
classes on graded Lie groups, within the range $1<p\leq 2 \leq q<\infty$.
Additionally, we present a sufficient condition for the $L^p$-$L^q$ estimates
of pseudo-differential operators within the range $1<p\leq q\leq 2$ or $2\leq
p\leq q<\infty$. The proofs rely on estimates of the Riesz and Bessel
potentials associated with Rockland operators, along with previously
established results on $L^p$-boundedness of global pseudo-differential
operators on graded Lie groups. Notably, as a byproduct, we also establish the
sharpness of the Sobolev embedding theorem for the inhomogeneous Sobolev spaces
on graded Lie groups.
