On interconnexion of two classes of functions being integrable on $$$[-1;1]$$$ with weight

S.V. Goncharov (Oles Honchar Dnipropetrovsk National University), https://orcid.org/0000-0002-8071-8746


We consider an interconnexion between two classes of functions being integrable with the weight, and satisfying conditions of Lipschitz type, in the integral metric, in certain cases.


integral metric; Lipschitz condition; weight function


Hardy G.H., Littlewood J.E. "A convergence criterion for Fourier series", Math. Zeitschr., 1928; 28: pp. 122-147.

Goncharov S.V. "On classes $$$\breve{H}^{(\nu)}_{p;\rho}$$$ and $$$\tilde{H}^{(\nu)}_{p;\rho}$$$", Dnipr. Univ. Math. Bull., 2011; 16: pp. 41-46. (in Russian)

Il'in V.P. "On one theorem of G.H. Hardy and J.E. Littlewood", Trudy MIAN SSSR, 1959; 53: pp. 128-144. (in Russian)

DOI: https://dx.doi.org/10.15421/241213



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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991