On the weak L 1 space and singular measures
Kaufman, Robert
Annales de l'Institut Fourier, Tome 32 (1982), p. 119-128 / Harvested from Numdam
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On construit des mesures singulières dont les sommes partielles de Fourier convergent vers zéro dans la métrique de L 1 -faible; on fait une analyse raffinée sur les ensembles symétriques de rapport constant.

We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak L 1 space; symmetric sets of constant ratio occur in an unexpected way.

@article{AIF_1982__32_1_119_0,
     author = {Kaufman, Robert},
     title = {On the weak $L^1$ space and singular measures},
     journal = {Annales de l'Institut Fourier},
     volume = {32},
     year = {1982},
     pages = {119-128},
     doi = {10.5802/aif.862},
     mrnumber = {84i:43006},
     zbl = {0464.42005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1982__32_1_119_0}
}

Kaufman, Robert. On the weak $L^1$ space and singular measures. Annales de l'Institut Fourier, Tome 32 (1982) pp. 119-128. doi : 10.5802/aif.862. http://gdmltest.u-ga.fr/item/AIF_1982__32_1_119_0/

[1] R. Kaufman, On transformations of exceptional sets, Bull. Greek Math. Soc., 18 (1977), 176-185. | MR 81g:43011 | Zbl 0438.43007

[2] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton, 1970. | MR 44 #7280 | Zbl 0207.13501

[3] A. Zygmund, Trigonometric Series, I, II, Cambridge, 1959 and 1968. | Zbl 0085.05601