We give weighted norm inequalities for the maximal fractional operator
${{\mathcal{M}}_{q}},\beta $ of Hardy–Littlewood and the fractional integral
${{I}_{\gamma }}$. These inequalities are established between
${{\left( {{L}^{q}},\,{{L}^{p}} \right)}^{\alpha }}\left( X,\,d,\,\mu \right)$ spaces (which are superspaces of Lebesgue spaces
${{L}^{\alpha }}\left( X,\,d,\,\mu \right)$ and subspaces of amalgams
$\left( {{L}^{q}},\,{{L}^{p}} \right)\left( X,d,\mu \right)$) and in the setting of space of homogeneous type
$\left( X,d,\mu \right)$. The conditions on the weights are stated in terms of Orlicz norm.