  In this paper we study the boundedness of global pseudo-differential
operators on smooth manifolds. By using the notion of global symbol we extend a
classical condition of H\"ormander type to guarantee the
$L^p$-$L^q$-boundedness of global operators. First we investigate
$L^p$-boundedness of pseudo-differential operators in view of the
H\"ormander-Mihlin condition. We also prove $L^\infty$-$BMO$ estimates for
pseudo-differential operators. Later, we concentrate our investigation to
settle $L^p$-$L^q$ boundedness of the Fourier multipliers and
pseudo-differential operators for the range $1<p \leq 2 \leq q<\infty.$ On the
way to achieve our goal of $L^p$-$L^q$ boundedness we prove two classical
inequalities, namely, Paley inequality and Hausdorff-Young-Paley inequality for
smooth manifolds. Finally, we present the applications of our boundedness
theorems to the well-posedness properties of different types of the nonlinear
partial differential equations.
