George Tephnadze

Martingale Hardy Spaces and Partial Sums and Fejér Means with Respect to the One-Dimensional Walsh-Fourier Series

abstract:
In this paper, we prove and discuss some new $(H_p,L_p)$ type inequalities for partial Sums and Fejér means with respect to the Walsh system. It is also proved that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

Mathematics Subject Classification: 42C10

Key words and phrases: Walsh group, Walsh system, $L_{p}$ space, weak-$L_{p}$ space, modulus of continuity, Walsh-Fourier coefficients, Walsh-Fourier series, partial sums, Lebesgue constants, Fejér means, dyadic martingale, Hardy space, maximal operator, strong convergence