  We study decompositions of Nakano type varying exponent Lebesgue norms and
spaces. These function spaces are represented here in a natural way as
tractable varying $\ell^p$ sums of projection bands. The main results involve
embedding the varying Lebesgue spaces to such sums, as well as the
corresponding isomorphism constants. The main tool applied here is an
equivalent variable Lebesgue norm which is defined by a suitable ordinary
differential equation introduced recently by the author. We also analyze the
effect of transformations changing the ordering of the unit interval on the
values of the ODE-determined norm.
