$ (L ^ {q}, \ ell ^ {p}) ^ {\ alpha} (G)$ spaces on a group of homogeneous type and continuity of the fractional integral.

We generalize in the context of locally compact group not necessarily abelian, a family of Banach spaces which are among other subspaces of Wiener amalgam spaces admitting an isometric dilation, and subspaces of spaces of Morrey . On these spaces, we establish weighted inequalities for the fractional maximal operator and the fractional integral.