Abstract
I t seems to be a general prinSiple t ha t theorems which are , ,Tauberian" in the sense of H a r d y and Litt lewood are mere corollaries of universal inequalities, which are valid for arbi t rary (rather than just for convergent) series and contain, therefore, absolute constants. In the present note the corresponding refinement of Tauber 's own theorem [3] will be deduced. Tauber 's theorem states tha t , in order t ha t a series a I + a 2 + . . 9 be convergent, its (A)-summabfli ty and the Cauchy-Kronecker condition
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