Geodesic
An Integral for Cesàro Summable Series
Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 85-97

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The pk+2 - integral of James [2] is strong enough to integrate a trigonometric series of the form 1.1 which is summable (C, k) in [0,2π], provided an extra condition holds involving the conjugate series 1.2 Considering series with coefficients o(n), Taylor [5] constructed an integral (the AP-integral) which successfully integrates series of the form (1. 1) which are Abel summable provided an extra condition holds involving the Abel means of the conjugate series (1.2). 
Cross, George. An Integral for Cesàro Summable Series. Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 85-97. doi: 10.4153/CMB-1967-010-1
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     author = {Cross, George},
     title = {An {Integral} for {Ces\`aro} {Summable} {Series}},
     journal = {Canadian mathematical bulletin},
     pages = {85--97},
     year = {1967},
     volume = {10},
     number = {1},
     doi = {10.4153/CMB-1967-010-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1967-010-1/}
}
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