Two-Dimensional Martingale Transforms and Their Applications in Summability of Walsh–Fourier Series

Ushangi Goginava, Károly Nagy

Research output: Contribution to journalArticlepeer-review

Abstract

In the paper, we are going to prove that the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series is bounded from Llog L((0 , 1] × (0 , 1]) to L1,((0 , 1] × (0 , 1]) . As a consequence, it can be obtained that Llog L((0 , 1] × (0 , 1]) is maximal Orlicz space, where the Nörlund logarithmic means of quadratic partial sums of two-dimensional Walsh–Fourier series for the functions from this space converge in measure.

Original languageEnglish
Article number245
JournalJournal of Geometric Analysis
Volume33
Issue number8
DOIs
Publication statusPublished - Aug 2023

Keywords

  • Dyadic martingale Hardy space
  • Marcinkiewicz means
  • Martingale transform
  • Nörlund logarithmic mean
  • Walsh system

ASJC Scopus subject areas

  • Geometry and Topology

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