New estimates for the B-Riesz transform

Abstract

In this paper, we study the B-Riesz transformation R-gamma((k)) generated by a generalized translation operator T-y (y is an element of R-+(n)). We prove that the Cotlar-type inequality holds for these operators. In particular, we prove results related to the Cotlar inequality for the even and odd cases of the kernel of the B-Riesz transform. Thus, new estimates for the B-Riesz transform in weighted Lebesgue spaces L-p,L-gamma,L-w are obtained.