Some estimates in GΓ(p,m,w) spaces

We consider a class of rearrangement invariant Banach Function Spaces recently appeared in a paper by the same authors, containing at the same time some Lorentz spaces Γ(ν), classical Lebesgue spaces and small Lebesgue spaces. We discuss the main properties coming directly from the norm, and, for certain values of the involved parameters, we prove some estimates of the norm of the associate space.