Summary
Author studies the summability (C,1+α+ρ) of the sequence nBn(x) under weaker conditions than those ofMinakishisundaram [3] and thus generalises his theorems. on the « Jump of a function » and by applying a tauberian theorem obtaing a criteria for the (C, α+ρ) summability of the conjugate series.
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Shrivastava, K.C. On the generalised jump of a function by its Fourier coefficients. Annali di Matematica 52, 349–362 (1960). https://doi.org/10.1007/BF02415679
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DOI: https://doi.org/10.1007/BF02415679