Article contents
Rearrangementsof the Haar system that preserve BMO
Published online by Cambridge University Press: 01 November 1997
Abstract
Let $\cal D $ denote the collection of dyadic intervals in the unit interval. Let $\tau$ be a rearrangement of the dyadic intervals. We study the induced operator
$$ Th_I = h_{\tau(I)}$$
where $h_I$ is the $L^{\infty}$ normalized Haar function. We find geometric conditions on $\tau$ which are necessary and sufficient for $T$ to be bounded on $BMO$. We also characterize the rearrangements of the $L^p$ normalized Haar system in $L^p.$
1991 Mathematics Subject Classification: 42C20, 43A17, 47B38.
- Type
- Research Article
- Information
- Proceedings of the London Mathematical Society , Volume 75 , Issue 3 , November 1997 , pp. 600 - 618
- Copyright
- London Mathematical Society 1997
- 1
- Cited by