Journal of Inequalities and Applications
Volume 6 (2001), Issue 4, Pages 415-433

On weighted dyadic Carleson’s inequalities

K. Tachizawa

Mathematical Institute, Tohoku University, Sendai 980-8578, Japan

Received 10 November 1999; Revised 2 February 2000

Copyright © 2001 K. Tachizawa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We give an alternate proof of weighted dyadic Carleson’s inequalities which are essentially proved by Sawyer and Wheeden. We use the Bellman function approach of Nazarov and Treil. As an application we give an alternate proof of weighted inequalities for dyadic fractional maximal operators. A result on weighted inequalities for fractional integral operators is given.