Quasiconvex uniform-convergence factors for Fourier series of functions with a given modulus of continuity |
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Authors: | S A Telyakovskii |
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Institution: | (1) V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR |
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Abstract: | It is proved that a quasiconvex sequence
v
of convergence factors transforms Fourier series of functions whose moduli of continuity do not exceed a given modulus of continuity (gd) into uniformly convergent series if and only if
n
(1/n) log n 0 for n ![rarr](/content/u538w261233q34n5/xxlarge8594.gif) . The sufficiency of this condition is already known.Translated from Matematicheskie Zametki, Vol. 8, No. 5,pp. 619–623, November, 1970. |
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