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

Lars-Erik Persson, George Tephnadze and Ferenc Weisz
Additional contact information
Lars-Erik Persson: UiT The Artic University of Norway
George Tephnadze: University of Georgia, School of Science and Technology
Ferenc Weisz: Eötvös Loránd University, Department of Numerical Analysis

Chapter Chapter 4 in Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series, 2022, pp 157-235 from Springer

Abstract: Abstract 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.

Date: 2022
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-14459-2_4

Ordering information: This item can be ordered from
http://www.springer.com/9783031144592

DOI: 10.1007/978-3-031-14459-2_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().