We consider a series of related extremal problems for holomorphic functions in a polydisc (Formula presented.), (Formula presented.). The sharp inequality (Formula presented.), with (Formula presented.), is established between the value of a functionholomorphic in (Formula presented.) and the norms of its limit values onmeasurable sets (Formula presented.), where (Formula presented.) and (Formula presented.) is the skeleton (the Shilov boundary) of (Formula presented.). This result is an analog of the two-constanttheorem by the Nevanlinna brothers. We study conditions under which the above inequalityprovides us with the value of the modulus of continuity of the functional for holomorphic extensionof a function on (Formula presented.) at a prescribed point of the polydisc. In thesecases, a solution was obtained of the problem of optimal recovery of a function from approximatelygiven values on a part of the skeleton (Formula presented.) and the relatedproblem of the best approximation of the functional of the continuation of a function into apolydisk from (Formula presented.) © 2023, Pleiades Publishing, Ltd.