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

References


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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Copyright (c) 2012 S.V. Goncharov

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