### Abstract

A general summability method, the so called θ-summability is considered for Gabor series. It is proved that the maximal operator of the θ-means defined in a cone is bounded from the local Hardy space h _{p} to L _{p} and from the amalgam space W (h _{p}, ℓ _{∞}) to W (L _{p}, ℓ∞). This implies the almost everywhere convergence of the θ-means for all f ∈ W (L _{1}, ℓ _{∞}).

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

Pages (from-to) | 255-284 |

Number of pages | 30 |

Journal | Sampling Theory in Signal and Image Processing |

Volume | 10 |

Issue number | 3 |

Publication status | Published - 2011 |

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### Keywords

- θ-summability
- Atomic decomposition
- Gabor expansions
- Gabor frames
- Local hardy spaces
- Time-frequency analysis
- Wiener amalgam spaces

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Computational Mathematics
- Radiology Nuclear Medicine and imaging

### Cite this

*Sampling Theory in Signal and Image Processing*,

*10*(3), 255-284.

**Gabor expansions and restricted summability.** / Weisz, F.

Research output: Contribution to journal › Article

*Sampling Theory in Signal and Image Processing*, vol. 10, no. 3, pp. 255-284.

}

TY - JOUR

T1 - Gabor expansions and restricted summability

AU - Weisz, F.

PY - 2011

Y1 - 2011

N2 - A general summability method, the so called θ-summability is considered for Gabor series. It is proved that the maximal operator of the θ-means defined in a cone is bounded from the local Hardy space h p to L p and from the amalgam space W (h p, ℓ ∞) to W (L p, ℓ∞). This implies the almost everywhere convergence of the θ-means for all f ∈ W (L 1, ℓ ∞).

AB - A general summability method, the so called θ-summability is considered for Gabor series. It is proved that the maximal operator of the θ-means defined in a cone is bounded from the local Hardy space h p to L p and from the amalgam space W (h p, ℓ ∞) to W (L p, ℓ∞). This implies the almost everywhere convergence of the θ-means for all f ∈ W (L 1, ℓ ∞).

KW - θ-summability

KW - Atomic decomposition

KW - Gabor expansions

KW - Gabor frames

KW - Local hardy spaces

KW - Time-frequency analysis

KW - Wiener amalgam spaces

UR - http://www.scopus.com/inward/record.url?scp=84865556596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865556596&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84865556596

VL - 10

SP - 255

EP - 284

JO - Sampling Theory in Signal and Image Processing

JF - Sampling Theory in Signal and Image Processing

SN - 1530-6429

IS - 3

ER -