Research output: Contribution to journal › Article › peer-review
In the present work, weighted Lp-norms of derivatives are studied in the spaces of entire functions script H signp(E) generalizing the de Branges spaces. A description of the spaces script H signp(E) such that the differentiation operator script D sign : F → F′ is bounded in script H signp(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 signp(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 signp(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 signp(E). Bibliography: 20 titles.
Original language | English |
---|---|
Pages (from-to) | 3927-3943 |
Number of pages | 17 |
Journal | Journal of Mathematical Sciences |
Volume | 129 |
Issue number | 4 |
DOIs | |
State | Published - 1 Sep 2005 |
ID: 32721584