Geodesic
The weighted $L^1$-integrability of functions and the Parseval equality with respect to multiplicative systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 15-26

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In this paper we prove necessary and sufficient conditions for the weighted $L^1$-integrability of functions defined on $[0,1)$ in terms of Fourier coefficients with respect to a multiplicative system of bounded type. These results are counterparts of trigonometric ones by M. and S. Izumi and M. M. Robertson.
Keywords: multiplicative systems of bounded type, weighted $L^1$-integrability, generalized monotonicity. 
@article{IVM_2012_8_a1,
     author = {S. S. Volosivets},
     title = {The weighted $L^1$-integrability of functions and the {Parseval} equality with respect to multiplicative systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--26},
     publisher = {mathdoc},
     number = {8},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_8_a1/}
}
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S. S. Volosivets. The weighted $L^1$-integrability of functions and the Parseval equality with respect to multiplicative systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2012), pp. 15-26. http://geodesic.mathdoc.fr/item/IVM_2012_8_a1/