Abstract
The main aim of this paper is to prove that there exists a martingale f ∈ H 1/2 such that the maximal Fejér operator with respect to Walsh-Kaczmarz system does not belong to the space L 1/2. For the two-dimensional case, we prove that there exists a martingale f ∈ H □ 1/2(f ∈ H 1/2) such that the restricted (unrestricted) maximal operator of Fejér means of two-dimensional Walsh-Kaczmarz-Fourier series does not belong to the space weak-L 1/2.
| Original language | English |
|---|---|
| Pages (from-to) | 181-200 |
| Number of pages | 20 |
| Journal | Journal of Function Spaces and Applications |
| Volume | 8 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2010 |
| Externally published | Yes |
Keywords
- Fejér means
- Hardy space
- Walsh Kaczmarz system
ASJC Scopus subject areas
- Analysis