István Mezö

Modulus of Continuity and Best Approximation with Respect to Vilenkin-Like
Systems in Some Function Spaces

We rephrase Fridli's result 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 (G\'{a}t, 2001) 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.

Modulus of continuity, best approximation, Vilenkin-like systems, logarithm space.

MSC 2000: 42C10