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Estimates of the L p -Norms of derivatives in spaces of entire functions. / Baranov, A. D.
в: Journal of Mathematical Sciences, Том 129, № 4, 01.09.2005, стр. 3927-3943.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Estimates of the L p -Norms of derivatives in spaces of entire functions
AU - Baranov, A. D.
PY - 2005/9/1
Y1 - 2005/9/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=23944433970&partnerID=8YFLogxK
U2 - 10.1007/s10958-005-0330-9
DO - 10.1007/s10958-005-0330-9
M3 - Article
AN - SCOPUS:23944433970
VL - 129
SP - 3927
EP - 3943
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 4
ER -
ID: 32721584