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 h p to L p and from the amalgam space W (h p , ∞ ) to W (L p , ∞ ). This implies the almost everywhere convergence of the θ -means for all f ∈ W (L 1 , ∞ ).