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Article overview
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Bellman approach to the one-sided bumping for weighted estimates of Calder'on--Zygmund operators | Fedor Nazarov
; Alexander Reznikov
; Alexander Volberg
; | Date: |
11 Jun 2013 | Abstract: | We give again (see also arXiv:1112.0676) a proof of weighted estimate of any
Calder’on-Zygmund operator. This is under a universal sharp sufficient
condition that is weaker than the so-called bump condition. Bump conjecture was
recently solved independently and simultaneously by A. Lerner (arXiv:1202.1860)
and Nazarov--Reznikov-Treil-Volberg (arXiv:1202.2406). The latter paper uses
the Bellman approach. Immediately a very natural and seemingly simple question
arises how to strengthen the bump conjecture result by weakening its
assumptions in a natural symmetric way. This is what we are dealing with here.
However we meet an unexpected and, in our opinion, deep obstacle, that allows
us to achieve only a partial result. The result of the present article is
slightly stronger than the one in arXiv:1112.0676. Our proof consists of two
main parts: reduction to a simple model operator, construction of Bellman
function for estimating this simple operator. The newer feature is that the
domain of definition of our Bellman function is infinitely dimensional. | Source: | arXiv, 1306.2653 | Services: | Forum | Review | PDF | Favorites |
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