A variation norm Carleson theorem for vector-valued Walsh Fourier series

作者：Hytonen Tuomas P^*; Lacey Michael T; Parissis Ioannis

来源：Revista Matematica Iberoamericana, 2014, 30(3): 979-1014.

DOI：10.4171/RMI/804

• Pointwise convergence
• variational norm
• Walsh-Fourier series

We prove a variation norm Carleson theorem for Walsh Fourier series of functions with values in certain UMD Banach spaces, sharpening a recent result of Hytonen and Lacey. They proved the point-wise convergence of Walsh Fourier series of X-valued functions under the qualitative hypothesis that X has some finite tile type q %26lt; infinity, which holds in particular if X is intermediate between another UMD space and a Hilbert space. Here we relate the precise value of the tile type index to the quantitative rate of convergence: tile type q of X is %26apos;almost equivalent%26apos; to the L-P-boundedness of the r-variation of the Walsh Fourier sums of any function f epsilon L-P([0, 1); X) for all r %26gt; q and large enough p.

• 出版日期2014