  In this paper we establish several Hardy and Hardy-Sobolev type inequalities
with homogeneous weights on the first orthant $\displaystyle
\mathbb{R}_{*}^n:=\{(x_1, \ldots, x_n):x_1>0, \ldots, x_n>0 \}$. We then use
some of them to produce Hardy type inequalities with remainder terms.
Furthermore, we obtain some interpolation inequalities and Maz'ya type
inequalities with remainder terms with the help of Maz'ya inequality and
Sobolev inequality of Cabr\'e and Ros-Orton on the upper half space
$\mathbb{R}_{+}^n:=\{x=(x_1, \ldots, x_n)|\, x_n>0 \}$.
