Extremizers and sharp weak-type estimates for positive dyadic shifts

We find the exact Bellman function for the weak L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2014-03, Vol.254, p.664-681
Main Authors: Rey, Guillermo, Reznikov, Alexander
Format: Article
Language:English
Subjects:
Bellman functions
Dyadic shifts
Sharp weak-type estimates
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Summary:We find the exact Bellman function for the weak L1 norm of local positive dyadic shifts. We also describe a sequence of functions, self-similar in nature, which in the limit extremize the local weak-type (1,1) inequality.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2013.12.030