A weighted $L^2$ estimate for the commutator of the Bochner-Riesz operator
نویسندگان
چکیده
منابع مشابه
Continuity for maximal commutator of Bochner-Riesz operators on some weighted Hardy spaces
which is the Bochner-Riesz operator (see [8]). Let E be the space E = {h : ‖h‖ = supr>0 |h(r)| <∞}, then, for each fixed x ∈ Rn, Bδ r ( f )(x) may be viewed as a mapping from [0,+∞) to E, and it is clear that Bδ ∗( f )(x) = ‖Bδ r ( f )(x)‖ and B ∗,b( f )(x) = ‖b(x)Bδ r ( f )(x)−Bδ r (b f )(x)‖. As well known, a classical result of Coifman et al. [4] proved that the commutator [b,T] generated by...
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For/e ¿"(R2), let (7£/)"(£) = (1 |£|2«2)î/(£). It is a well-known theorem of Carleson and Sjölin that T" defines a bounded operator on Z,4 if a > 0. In this paper we obtain an explicit weighted inequality of the form / sup \T%f(x)\2w(x)dxti( \f\2Paw(x)dx, 0 0. This strengthens the above theorem of Carleson and Sjölin. The method gives information on the maximal...
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for some fixed large N0; we shall call such weights admissible. Rubio de Francia [11] showed that for every w ∈ L(R) there is a nonnegative W ∈ L(R) such that ‖W‖2 ≤ Cλ‖w‖2, Cλ < ∞ if λ > 0, and the analogous weighted norm inequality for S t holds uniformly in t. He used methods related to factorization theory of operators and the proof gave no information on how to construct w from W . In [3] ...
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متن کاملA Proof of the Bochner-riesz Conjecture
For f ∈ S(R), we consider the Bochner-Riesz operator R of index δ > 0 defined by R̂δf(ξ) = (1− |ξ|)+ f̂(ξ). Then we prove the Bochner-Riesz conjecture which states that if δ > max{d|1/p − 1/2| − 1/2, 0} and p > 1 then R is a bounded operator from L(R) into L(R); moreover, if δ(p) = d(1/p − 1/2) − 1/2 and 1 < p < 2d/(d + 1), then Rδ(p) is a bounded operator from L(R) into L(R).
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1997
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-97-03882-3