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arXiv · 1202.0209

Pointwise convergence of Walsh--Fourier series of vector-valued functions

Tuomas P. Hytönen·Michael T. Lacey
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Abstract

We prove a version of Carleson's Theorem in the Walsh model for vector-valued functions: For $1<p< \infty$, and a UMD space $Y$, the Walsh-Fourier series of $f \in L ^{p}(0,1;Y)$ converges pointwise, provided that $Y$ is a complex interpolation space $Y=[X,H]_\theta$ between another UMD space $X$ and a Hilbert space $H$, for some $\theta\in(0,1)$. Apparently, all known examples of UMD spaces satisfy this condition.

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Tuomas P. Hytönen, Michael T. Lacey. 2012-02-01. Pointwise convergence of Walsh--Fourier series of vector-valued functions. https://doi.org/10.4310/mrl.2018.v25.n2.a11

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