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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generalised Lipschitz class of functions and the absolute summability of Fourier series by Nörlund means


Authors: S. N. Lal and K. N. Singh
Journal: Proc. Amer. Math. Soc. 81 (1981), 41-49
MSC: Primary 42A28; Secondary 40F05, 40G05
MathSciNet review: 589133
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Abstract: The main aim of the paper is to investigate the relationship between certain generalised Lipschitz classes of functions and to discuss the absolute Nörlund summability of Fourier series of functions of the class $ {L^q}$ where $ 2 < q < \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0589133-5
PII: S 0002-9939(1981)0589133-5
Keywords: Class $ {\text{Lip}}(\alpha ,q)$, convergence almost everywhere, conjugate function, summable $ \left\vert {N,{p_n}} \right\vert$, maximum modulus
Article copyright: © Copyright 1981 American Mathematical Society