Resumen de The Segal Algebra S0(\Bbb Rd) and Norm Summability of Fourier Series and Fourier Transforms

Hans G. Feichtinger, Ferenc Weisz

• A general summability method, the so-called ?-summability is considered for multi-dimensional Fourier series. Equivalent conditions are derived for the uniform and L 1-norm convergence of the ?-means s n ? f to the function f. If f is in a homogeneous Banach space, then the preceeding convergence holds in the norm of the space. In case ? is an element of Feichtinger¿s Segal algebra , then these convergence results hold. Some new sufficient conditions are given for ? to be in . A long list of concrete special cases of the ?-summation is listed. The same results are also provided in the context of Fourier transforms, indicating how proofs have to be changed in this case