In the present work, weighted L~p -norms of derivatives are studied in the spaces of entire functions H~p(E) generalizing the de Branges spaces. A description of the spaces H~p(E) such that the differentiation operator D : F → F′ is bounded in H~p(E) is obtained in terms of the generating entire function E of the Hermite-Biehler class. It is shown that for a broad class of the spaces H~p(E), the boundedness criterion is given by the condition E′/E ∈ L~∞(R). In the general case, a necessary and sufficient condition is found in terms of a certain embedding theorem for the space H~p(E); moreover, the boundedness of the operator D depends essentially on the exponent p. We obtain a number of conditions sufficient for the compactness of the differentiation operator in H~p (E).
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