ON A PROPERTY OF GENERAL HAAR SYSTEM

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Submitted: 2025-02-17; Published: 2025-02-17

This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

Abstract

In the paper we prove that for some type of general Haar systems (particularly for classical Haar system) and for any ε>0 there exists a set {E⊂(0,1)2,|E|>1−ε}, such that for every f∈L1(0,1)2 one can find a function g∈L1(0,1)2, which coincides with f on E and Fourier--Haar coefficients {c(i,k)(g)}i,k=1∞ are monotonic over all rays.