Geodesic
Integration of Banach-valued functions and Haar series with Banach-valued coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 25-32 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of a Henstock type integral with respect to dyadic derivation basis. At the same time convergence of Fourier–Henstock–Haar series Banach-space-valued functions is essentially dependent on properties of a space. 
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V. A. Skvortsov. Integration of Banach-valued functions and Haar series with Banach-valued coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2017), pp. 25-32. http://geodesic.mathdoc.fr/item/VMUMM_2017_1_a3/

[1] Hytonen T., Lacey M., “Pointwise convergence of vector-valued Fourier series”, Math. Ann., 357 (2013), 1329–1361 | DOI | MR | Zbl

[2] Hytonen T., Lacey M., Pointwise convergence of Walsh-Fourier series of vector-valued functions, 1 Feb 2012, arXiv: 1202.0209v1 [math.CA] | MR

[3] Blasco O., Signes T., “Q-concavity and q-Orlicz property on symmetric sequence spaces”, Taiwan. J. Math., 5 (2001), 331–352 | DOI | MR | Zbl

[4] Skvortsov V.A., “Henstock–Kurzweil type integrals in P-adic harmonic analysis”, Acta Math. Acad. Paedagog. Nyhazi, 20 (2004), 207–224 | MR | Zbl

[5] Golubov B.I., Efimov A.V., Skvortsov V.A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR

[6] Lukashenko T.P., Skvortsov V.A., Solodov A.P., Obobschennye integraly, URSS, M., 2010

[7] Ostaszewski K.M., Henstock integration in the plane, Mem. AMS, 63, no. 353, 1986 | MR

[8] Thomson B.S., “Derivation bases on the real line”, Real Anal. Exchange, 8:1 (1982/83), 67–207 ; 2, 278–442 | MR | MR

[9] Skvortsov V.A., Tulone F., “$\mathcal P$-ichnyi integral Khenstoka v teorii ryadov po sistemam kharakterov nul-mernykh grupp”, Vestn. Mosk. un-ta. Matem. Mekhan., 2006, no. 1, 25–29 | Zbl

[10] Schwabik S., Ye Guoju, Topics in Banach space integration, Series in Real Analysis, 10, World Scientific, Hackensack, NJ, 2005 | MR | Zbl

[11] Plotnikov M.G., “Kvazimery, khausdorfovy $p$-mery i ryady Uolsha i Khaara”, Izv. RAN. Ser. matem., 74:4 (2010), 157–188 | DOI | MR | Zbl

[12] Skvortsov V., Tulone F., “Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series”, J. Math. Anal. and Appl., 421:2 (2015), 1502–1518 | DOI | MR | Zbl

[13] Dilworth S.J., Girardi M., “Nowhere weak differentiability of the Pettis integral”, Quaest. Math., 18:4 (1995), 365–380 | DOI | MR | Zbl