no. 1
On the weak L 1 space and singular measures
Annales de l'Institut Fourier, Tome 32 (1982) no. 1, pp. 119-128.

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.

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     author = {Kaufman, Robert},
     title = {On the weak $L^1$ space and singular measures},
     journal = {Annales de l'Institut Fourier},
     pages = {119--128},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {32},
     number = {1},
     year = {1982},
     doi = {10.5802/aif.862},
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Kaufman, Robert. On the weak $L^1$ space and singular measures. Annales de l'Institut Fourier, Tome 32 (1982) no. 1, pp. 119-128. doi : 10.5802/aif.862. https://aif.centre-mersenne.org/articles/10.5802/aif.862/

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

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

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

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