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

S.V. Goncharov

doi:10.15421/241213

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

Abstract

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.

Keywords

integral metric; Lipschitz condition; weight function

Full Text:

PDF (Русский)

References

Hardy G.H., Littlewood J.E. "A convergence criterion for Fourier series", Math. Zeitschr., 1928; 28: pp. 122-147. doi:10.1007/BF01181186

Goncharov S.V. "On classes $$$\breve{H}^{(\nu)}_{p;\rho}$$$ and $$$\tilde{H}^{(\nu)}_{p;\rho}$$$", Res. Math., 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)