On classes $$$\breve{H}_{p; \rho}^{(\nu)}$$$ and $$$\widetilde{H}_{p; \rho}^{(\nu)}$$$

S.V. Goncharov

doi:10.15421/241107

On classes $$$\breve{H}_{p; \rho}^{(\nu)}$$$ and $$$\widetilde{H}_{p; \rho}^{(\nu)}$$$

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

Abstract

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

Keywords

integral metric; Lipschitz condition

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References

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

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://doi.org/10.15421/241107