  We consider fractional quantum Hall states built on Laughlin's original
N-body wave-functions, i.e., they are of the form holomorphic times gaussian
and vanish when two particles come close, with a given polynomial rate. Such
states appear naturally when looking for the ground state of 2D particles in
strong magnetic fields, interacting via repulsive forces and subject to an
external potential due to trapping and/or disorder. We prove that all functions
in this class satisfy a universal local density upper bound, in a suitable weak
sense. Such bounds are useful to investigate the response of fractional quantum
Hall phases to variations of the external potential. Contrary to our previous
results for a restricted class of wave-functions, the bound we obtain here is
not optimal, but it does not require any additional assumptions on the
wave-function, besides analyticity and symmetry of the pre-factor modifying the
Laughlin function.
