Journal of Operator Theory

Volume 32, Issue 2, Fall 1994 pp. 243-254.

Boundedness of some singular integral operators in weighted $L^2$ spaces

Authors: Takanori Yamamoto
Author institution:Department of Mathematics, Hokkai-Gakuen University, Sapporo 062, JAPAN

Summary: In the previous paper, when measurable functions $\alpha$, $\beta$ and a weight function $W$ satisfy some conditions, we gave the necessary and sufficient condition of the boundedness of singular integral operators $\alpha{P_+} + \beta{P_\_}$ in the weighted norm of $L^2(W)$, where $P_+$ is an analytic projection and $P_\_$ is a co-analytic projection. In this paper, we give it completely in general.

Keywords: Hardy spaces, singular integral operators, analytic projections, weighted norm inequalities.

Contents Full-Text PDF