In the present paper, we defined and then studied Hardy spaces related to spherical mean operators. We proved Hardy-type inequalities, then we showed refined Sobolev-type inequalities between homogeneous Riesz-type spaces, homogeneous Besov-type spaces, and Lorentz-type spaces. Next, we introduced and studied Hausdorff operators on generalized Hardy spaces. Finally, we investigated maximal Bochner-Riesz operators on generalized Hardy spaces.