A VARIATION NORM CARLESON THEOREM FOR VECTOR-VALUED WALSH-FOURIER SERIES
A VARIATION NORM CARLESON THEOREM FOR VECTOR-VALUED WALSH-FOURIER SERIES
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DOI：
10.4171/rmi/804
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发表时间：
2012-09
影响因子：
1.2
通讯作者：
T. Hytonen;M. Lacey;I. Parissis
中科院分区：
文献类型：
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作者：
T. Hytonen;M. Lacey;I. Parissis
本文证明了UMD Banach空间中带值函数的Walsh-Fourier级数的一个变范数Carleson定理。我们对巴拿赫空间的唯一假设是它具有有限瓦片型，这是Hytonen和Lacey引入的概念。给定q∈(2,∞)，我们证明，如果空间X对所有τ∈(q,∞)具有瓦片类型τ，则任意函数f∈L p ((0,1)；对于介于UMD空间Y和Hilbert空间H之间的复插值空间，即空间X = (Y，H)θ，其瓦片类型为q = 2/θ。我们证明，在这种情况下，变范数Carleson定理在更大范围> (2r/q) '中对所有b> q仍然成立。
We prove a variation norm Carleson theorem for Walsh-Fourier series of func- tions with values in a UMD Banach space. Our only hypothesis on the Banach space is that it has finite tile-type, a notion introduced by Hytonen and Lacey. Given q ∈ (2,∞) we show that, if the space X has tile-typeτ for allτ ∈ (q,∞) then the r-variation of the Walsh-Fourier sums of any function f ∈ L p ((0,1);X) belongs to L p , whenever q q. For intermediatespaces, i.e. spacesX = (Y,H)θ which arecomplex interpolation spaces between some UMD space Y and a Hilbert space H, the tile-type is q = 2/θ. We show that in this case the variationnorm Carleson theoremremains true for allr> q in the largerrangep> (2r/q) ' .