Summability of Gabor expansions and Hardy spaces

New Wiener amalgam spaces are introduced for local Hardy spaces. 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 is bounded from hp to Lp and from the amalgam space W(hp,ℓ∞) to W(Lp,ℓ∞). This implies the almost everywhere convergence of the θ-means for all f∈W(L1,ℓ∞).