Pointwise convergence of Walsh-Fourier series of vector-valued functions
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Hytönen , T P & Lacey , M T 2018 , ' Pointwise convergence of Walsh-Fourier series of vector-valued functions ' , Mathematical Research Letters , vol. 25 , no. 2 , pp. 561–580 . https://doi.org/10.4310/MRL.2018.v25.n2.a11
| Titel: | Pointwise convergence of Walsh-Fourier series of vector-valued functions |
| Författare: | Hytönen, Tuomas P.; Lacey, Michael T. |
| Medarbetare: | University of Helsinki, Department of Mathematics and Statistics |
| Datum: | 2018 |
| Språk: | eng |
| Sidantal: | 20 |
| Tillhör serie: | Mathematical Research Letters |
| ISSN: | 1073-2780 |
| Permanenta länken (URI): | http://hdl.handle.net/10138/307037 |
| Abstrakt: | We prove a version of Carleson’s Theorem in the Walsh model for vector-valued functions: For 1<p<∞, and a UMD space Y, the Walsh–Fourier series of f∈Lp(0,1;Y) converges pointwise, provided that Y is a complex interpolation space Y=[X,H]θ between another UMD space X and a Hilbert space H, for some θ∈(0,1). Apparently, all known examples of UMD spaces satisfy this condition. |
| Subject: | 111 Mathematics |
| Licens: |
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