Geodesic
Fractional Integrals of Imaginary Order in the Space of Hölder Functions with Polynomial Weight on an Interval
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 52-59

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We study fractional integrals of imaginary order in the Marchaud form in Hölder space with polynomial weight at finitely many points in the closed interval $[0,1]$. We present conditions on the orders of the weight for which this operator is invertible in the space described above. 
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     author = {N. K. Karapetyants and L. D. Shankishvili},
     title = {Fractional {Integrals} of {Imaginary} {Order} in the {Space} of {H\"older} {Functions} with {Polynomial} {Weight} on an {Interval}},
     journal = {Matemati\v{c}eskie zametki},
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N. K. Karapetyants; L. D. Shankishvili. Fractional Integrals of Imaginary Order in the Space of Hölder Functions with Polynomial Weight on an Interval. Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 52-59. http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a5/