### Abstract

A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ_{1})(ℝ^{d}). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the H_{p} Hardy space to L_{p} (or H_{p}). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

Original language | English |
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Pages (from-to) | 419-442 |

Number of pages | 24 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 145 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 2008 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Wiener amalgams, Hardy spaces and summability of Fourier series.** / Weisz, F.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Wiener amalgams, Hardy spaces and summability of Fourier series

AU - Weisz, F.

PY - 2008/9

Y1 - 2008/9

N2 - A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

AB - A general summability method, the so called θ-summability is considered for multi-dimensional Fourier series, where θ is in the Wiener algebra W(C,ℓ1)(ℝd). It is based on the use of Wiener amalgam spaces, weighted Feichtinger's algebra, Herz and Hardy spaces. Under some conditions on θ, it is proved that the maximal operator of the θ-means is bounded from the Hp Hardy space to Lp (or Hp). This implies some norm and almost everywhere convergence results for the θ-means. Large number of special cases of the θ-summation are considered.

UR - http://www.scopus.com/inward/record.url?scp=49549093404&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549093404&partnerID=8YFLogxK

U2 - 10.1017/S0305004108001448

DO - 10.1017/S0305004108001448

M3 - Article

VL - 145

SP - 419

EP - 442

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 2

ER -