Extremizers and sharp weak-type estimates for positive dyadic shifts

Guillermo Rey; Alexander Reznikov

doi:10.1016/j.aim.2013.12.030

paper

Extremizers and sharp weak-type estimates for positive dyadic shifts

arXiv:1311.2046 · doi:10.1016/j.aim.2013.12.030

Abstract

We find the exact Bellman function for the weak $L^{1}$ 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.

Fixed two minor typos. To appear in Advances in Mathematics

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