### 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 |
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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 - Dec 1 2011 |

### Keywords

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

### ASJC Scopus subject areas

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

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## Cite this

Weisz, F. (2011). Gabor expansions and restricted summability.

*Sampling Theory in Signal and Image Processing*,*10*(3), 255-284.