Geodesic
Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 3-13

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We consider a convolution operator in spaces of holomorphic functions in a convex domain of the complex plane with polynomial growth at a boundary. We proved that if this operator is surjective on the class of all bounded convex domains, then it always has a linear continuous right inverse operator.
Keywords: holomorphic function, polynomial growth, convolution operator, linear continuous right/left inverse operator. 
@article{IVM_2015_1_a0,
     author = {A. V. Abanin and Le Hai Khoi},
     title = {Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--13},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_1_a0/}
}
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A. V. Abanin; Le Hai Khoi. Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 3-13. http://geodesic.mathdoc.fr/item/IVM_2015_1_a0/