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This paper addresses the optimal recovery of functions from Hilbert spaces of functions on the unit disc. The estimation, or recovery, is performed from inaccurate information given by integration along radial paths. For a holomorphic function expressed as a series, three distinct situations are considered: where the information error in L2 norm is bound by δ0 or for a finite number of terms the error in l2N norm is bound by δ0 or lastly the error in the jth coefficient is bound by δj0. The results are applied to the Hardy-Sobolev and Bergman-Sobolev spaces

Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration