Research Article

Some properties of the Walsh-Nörlund means

Published in: Quaestiones Mathematicae
Volume 46 , issue 2 , 2023 , pages: 301–334

DOI: 10.2989/16073606.2021.2014594

Author(s): Ushangi Goginava United Arab Emirates University, UAE , Károly Nagy Institute of Mathematics and Computer Sciences, University of Nyíregyháza, Nyíregyháza, Hungary

Keywords: 42C10 , Walsh system , Nörlund mean , Fejér mean , martingale transform , weak type inequality , convergence in norm , almost everywhere convergence

Download full text Get new issue alerts

Abstract

In the present paper we give a necessary and suﬃcient condition on monotone weights, which guaranties the Nörlund means of Walsh-Fourier series converge in L ₁ norm and C_W norm. We also discuss the almost everywhere summability by Nörlund means and we prove that our condition is suﬃcient for almost everywhere convergence of Nörlund means for all integrable functions.

« New approach to property (ω) for functions of operators

Further results on the independent Roman domination number of graphs »