The centered Hardy Littlewood function M_c f and the centered HLW w.r.t. cubes M_c f' are comparable, i.e. there exist positive constants a and b such that
a M_c ' f <= M_c f<= b M_c' f (A)
Can we say the same about the uncentered HLW functions M_u and M_u ' ?
' indicates w.r.t. cubes
I know that M_c is weak (1,1) so by (A), I can say that M_c' is weak (1,1) as well.
But how do I conclude from (A) that M_u and M_u' are weak (1,1) as well?