# lacunary Walsh series in rearrangement invariant spaces

## TL;DR

This paper extends classical results about Rademacher systems in rearrangement invariant spaces to lacunary Walsh series, showing similar subspace properties hold for these series.

## Contribution

It demonstrates that properties known for Rademacher systems also apply to lacunary Walsh series within rearrangement invariant spaces, broadening the scope of these classical results.

## Key findings

- Classical results extend to lacunary Walsh series
- Subspace properties hold for lacunary Walsh series
- Similar behavior as Rademacher systems in rearrangement invariant spaces

## Abstract

We prove that the classical results by Rodin and Semenov and by Lindenstrauss and Tzafriri on the subspace generated by the Rademacher system in rearrangement invariant spaces also hold for lacunary Walsh series.