Article contents
Two remarks on primary spaces
Published online by Cambridge University Press: 07 June 2012
Abstract
We prove that for an operator T on ℓ∞(H1 ()), respectively ℓ∞(L1 ()), the identity factors through T or Id - T. Hence ℓ∞(H1 ()) and ℓ∞(L1 ()) are primary spaces. We re-prove analogous results of H.M. Wark for the spaces ℓ∞(Hp()), 1 < p < ∞. In the present paper direct combinatorics of colored dyadic intervals replaces the dependence on Szemerédi's theorem in [11].
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 153 , Issue 3 , November 2012 , pp. 505 - 523
- Copyright
- Copyright © Cambridge Philosophical Society 2012
References
REFERENCES
- 5
- Cited by