### Abstract

It is proved that the maximal operator σδ# of the triangular-Fejér-means of a two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 > p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σδ _{2n} of a function f ∈ L1 converge a.e. to f . The maximal operator σδ# is bounded from the Hardy space H _{1/2} to the space weak-L _{1/2} and is not bounded from the Hardy space H _{1/2} to the space L _{1/2}.

Original language | English |
---|---|

Pages (from-to) | 101-115 |

Number of pages | 15 |

Journal | Georgian Mathematical Journal |

Volume | 19 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2012 |

### Fingerprint

### Keywords

- Hardy space
- Maximal operator
- Triangular partial sums
- Walsh function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Maximal operator of the Fejér means of triangular partial sums of two-dimensional WalshFourier series.** / Goginava, Ushangi; Weisz, F.

Research output: Contribution to journal › Article

*Georgian Mathematical Journal*, vol. 19, no. 1, pp. 101-115. https://doi.org/10.1515/gmj-2012-0004

}

TY - JOUR

T1 - Maximal operator of the Fejér means of triangular partial sums of two-dimensional WalshFourier series

AU - Goginava, Ushangi

AU - Weisz, F.

PY - 2012/3

Y1 - 2012/3

N2 - It is proved that the maximal operator σδ# of the triangular-Fejér-means of a two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 > p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σδ 2n of a function f ∈ L1 converge a.e. to f . The maximal operator σδ# is bounded from the Hardy space H 1/2 to the space weak-L 1/2 and is not bounded from the Hardy space H 1/2 to the space L 1/2.

AB - It is proved that the maximal operator σδ# of the triangular-Fejér-means of a two-dimensional Walsh-Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 > p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σδ 2n of a function f ∈ L1 converge a.e. to f . The maximal operator σδ# is bounded from the Hardy space H 1/2 to the space weak-L 1/2 and is not bounded from the Hardy space H 1/2 to the space L 1/2.

KW - Hardy space

KW - Maximal operator

KW - Triangular partial sums

KW - Walsh function

UR - http://www.scopus.com/inward/record.url?scp=84860518619&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860518619&partnerID=8YFLogxK

U2 - 10.1515/gmj-2012-0004

DO - 10.1515/gmj-2012-0004

M3 - Article

AN - SCOPUS:84860518619

VL - 19

SP - 101

EP - 115

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

SN - 1572-9176

IS - 1

ER -