Estimation of norms of singular integral operators in \(L^ p\) spaces with weights, satisfying Muckenhoupt's condition (Q578562)

There are considered spaces \(L^ p(R^ n;w)\), \(p>1\), with the norm \(\| f\|_{p,w}=(\int_{R^ n}| f(x)|^ pw(x)dx)^{1/p}\) in the case when the weights w satisfy the following condition, called the Muckenhoupt condition: \[ \int_{Q}w(x)dx(\int_{Q}w^{-(p-1)-1}(x)dx)^{p-1}\leq K_ p| Q|^ p \] for an arbitrary cube \(Q\subset R^ n\), with a constant \(K_ p\) which does not depend on Q. There are given some estimations of norms of Calderon-Zygmund operators in these spaces.