Estimates of the L p -Norms of derivatives in spaces of entire functions

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Estimates of the L ^p -Norms of derivatives in spaces of entire functions. / Baranov, A. D.

In: Journal of Mathematical Sciences, Vol. 129, No. 4, 01.09.2005, p. 3927-3943.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{a63e53bee7c74e9ca52db088e9625f2f,

title = "Estimates of the L p -Norms of derivatives in spaces of entire functions",

abstract = "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.",

author = "Baranov, {A. D.}",

year = "2005",

month = sep,

day = "1",

doi = "10.1007/s10958-005-0330-9",

language = "English",

volume = "129",

pages = "3927--3943",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

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