Geodesic
On properties of certain classical operators occurring in Fourier analysis
Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1395-1412

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Properties of conjugate functions, Hilbert transforms, and certain maximal operators occurring in Fourier analysis in weighted Lebesgue spaces are established. For functions of several variables in Orlicz spaces the divergence in measure of the Cesáro and the Abel means of the conjugate trigonometric series, and the question of the existence of conjugate functions are investigated. 
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     author = {L. V. Zhizhiashvili and G. E. Tkebuchava},
     title = {On properties of certain classical operators occurring in {Fourier} analysis},
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L. V. Zhizhiashvili; G. E. Tkebuchava. On properties of certain classical operators occurring in Fourier analysis. Sbornik. Mathematics, Tome 195 (2004) no. 10, pp. 1395-1412. http://geodesic.mathdoc.fr/item/SM_2004_195_10_a0/