Nörlund and T Means of Vilenkin-Fourier Series in Lebesgue Spaces

The n-th Nörlund and Riesz logarithmic means are defined by Nörlund logarithmic mean Riesz logarithmic mean Ln f Rn f L n f = : 1 l n ∑ k = 0 n − 1 S k f n − k $$\displaystyle \begin{aligned} L_nf=:\frac{1}{l_n}\sum_{k=0}^{n-1}\frac{S_kf}{n-k} \end{aligned}$$ and R n f = : 1 l n ∑ k = 1 n S k f k , $$\displaystyle \begin{aligned} R_nf=:\frac{1}{l_n}\sum_{k=1}^{n}\frac{S_kf}{k}, \end{aligned}$$ respectively, where ln l n = : ∑ k = 1 n 1 k . $$\displaystyle \begin{aligned} l_n=:\sum_{k=1}^{n}\frac{1}{k}. \end{aligned}$$ It is known that the Nörlund logarithmic means have better approximation properties than the partial sums and that the Riesz logarithmic means are better than Fejér means in the same sense.