Abstract:We consider spherical Riesz means of multiple Fourier series and some generalizations. While almost everywhere convergence of Riesz means at the critical index (d − 1)/2 may fail for functions in the Hardy space h 1 (T d ), we prove sharp positive results for strong summability almost everywhere. For functions in L p (T d ), 1 < p < 2, we consider Riesz means at the critical index d(1/p − 1/2) − 1/2 and prove an almost sharp theorem on strong summability. The results follow via transference from corresponding … Show more
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