On the logarithmic summability $(L,1)$ of integrals on $[1,\infty)$
Résumé
Moricz [Analysis (Munich) 18(1) (1998), 1-8] characterized summability (C,1) of integrals by convergence of another integral. In this work, we extend this result to logarithmic summability (L,1) of integrals.
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Références
Hardy, G. H., A theorem concerning summable series, Proc. Cambridge Philosoph. Soc. 20, 304-307, (1920-21).
Moricz, F., Summability (C, 1) of integrals on R+, Analysis (Munich). 18(1), 1-8, (1998). DOI: https://doi.org/10.1524/anly.1998.18.1.1
Moricz, F., Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences, Studia Math. 219(2), 109-121, (2013). DOI: https://doi.org/10.4064/sm219-2-2
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