Geodesic
On the Kolmogorov theorems on Fourier series and conjugate functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 21-34

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We consider Fourier series of summable functions from spaces wider than $L_1$. We describe classes $\varphi(L)$ which contain conjugate functions, where their conjugate Fourier series converge. The obtained results are more general than the A. N. Kolmogorov theorems on the convergence of Fourier series in metrics weaker than $L_1$.
Keywords: Fourier series, conjugate functions, generalized Orlicz spaces, classes $\varphi(L)$. 
@article{IVM_2012_7_a2,
     author = {V. I. Filippov},
     title = {On the {Kolmogorov} theorems on {Fourier} series and conjugate functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {21--34},
     publisher = {mathdoc},
     number = {7},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_7_a2/}
}
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V. I. Filippov. On the Kolmogorov theorems on Fourier series and conjugate functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2012), pp. 21-34. http://geodesic.mathdoc.fr/item/IVM_2012_7_a2/