In the present work, weighted L^p-norms of derivatives are studied in the spaces of entire functions script H sign^p(E) generalizing the de Branges spaces. A description of the spaces script H sign^p(E) such that the differentiation operator script D sign : F → F′ is bounded in script H sign^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 script H sign^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 script H sign^p(E); moreover, the boundedness of the operator script D sign depends essentially on the exponent p. We obtain a number of conditions sufficient for the compactness of the differentiation operator in script H sign^p(E). Bibliography: 20 titles.