An observation: cut-off of the weight $w$ does not increase the $A_{p_1,p_2}$-"norm'' of $w$

Alexander Reznikov, Vasiliy Vasyunin, Alexander Volberg

We consider weights $w$ and their cut-offs: $w_a(t)=w(t)$ if $w(t)\le a$ and $w_a(t)=a$ if $w(t)>a$. We consider a generalized $A_p$-``norm'' and prove that the ``norm'' of $w_a$…