On systems of non-overlapping Haar polynomials

We prove that $\operatorname{log} n$ is an almost everywhere convergence Weyl multiplier for the orthonormal systems of non-overlapping Haar polynomials. Moreover, it is done for the general systems of martingale difference polynomials.

Keywords

Haar system, martingale difference, non-overlapping polynomials, Weyl multiplier, Menshov–Rademacher theorem

2010 Mathematics Subject Classification

42C05, 42C10, 42C20

Full Text (PDF format)

Research was supported by the Science Committee of Armenia, grant 18T-1A081.

Received 19 February 2019

Received revised 4 October 2019

Accepted 18 October 2019

Published 21 July 2022