  Fusion frames enable signal decompositions into weighted linear subspace
components. For positive integers p, we introduce p-fusion frames, a sharpening
of the notion of fusion frames. Tight p-fusion frames are closely related to
the classical notions of designs and cubature formulas in Grassmann spaces and
are analyzed with methods from harmonic analysis in the Grassmannians. We
define the p-fusion frame potential, derive bounds for its value, and discuss
the connections to tight p-fusion frames.
