# An observation: cut-off of the weight $w$ does not increase the $A {p {1}, p {2}}$-norm&#x27;&#x27; of $w$ - Mathematics > Analysis of PDEs

An observation: cut-off of the weight $w$ does not increase the $A {p {1}, p {2}}$-norm&#x27;&#x27; of $w$ - Mathematics > Analysis of PDEs - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider weights $w$ and their cut-offs: $w at=wt$ if $wt\le a$ and$w at=a$ if $wt> a$. 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.

Author: Alexander Reznikov, Vasiliy Vasyunin, Alexander Volberg

Source: https://arxiv.org/