Georgian Mathematical Journal 13 (2006), No. 2, 315--332
Copyright Heldermann Verlag 2006
Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like Systems in Some Function Spaces
István Mezö
Vincellér str. 2, Debrecen, Hungary
mistvan4@hotmail.com
We rephrase the result of S. Fridli [Acta Math. Hungar. 45 (1985) 393--396] on the modulus of continuity with respect to a Vilenkin group in the Lebesgue space. We show that this result is valid in the logarithm space and for Vilenkin-like systems. In addition, we prove that there is a strong connection between the best approximation of Fourier series and the modulus of continuity, not only in the Lebesgue space [see G. Gát, Acta Math. Acad. Paedagog. Nyhzi (N.S.) 17 (2001) 161--169] but in the logarithm space too. We formulate two variable generalizations of the obtained results, which have not been known till now even in the Walsh case.
Keywords: Modulus of continuity, best approximation, Vilenkin-like systems, logarithm space.
MSC: 42C10
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