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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 provethat the ``norm'' of $w_a$ is not greater then the ``norm'' of $w$. Our proofin the case $w\in A_2$ is especially simple.

An observation: cut-off of the weight $w$ does not increase the $A_{p_{1}, p_{2}}$-"norm'' of $w$