New multi-dimensional Wiener amalgam spaces (Formula presented.)(Rd) are introduced by taking the usual one-dimensional spaces coordinatewise in each dimension. The strong Hardy-Littlewood maximal function is investigated on these spaces. The pointwise convergence in Pringsheim’s sense of the θ-summability of multi-dimensional Fourier transforms is studied. It is proved that if the Fourier transform of θ is in a suitable Herz space, then the θ-means (Formula presented.) converge to f a.e. for all (Formula presented.)(Rd). Note that (Formula presented.) and (Formula presented.), where 1<r≤∞. Moreover, (Formula presented.) converges to f(x) at each Lebesgue point of (Formula presented.).
- Herz spaces
- Lebesgue points
- Strong Hardy-Littlewood maximal function
- Wiener amalgam spaces
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