Fourier cosine and sine transforms and generalized Lipschitz classes in the uniform metric

• Published in: Український математичний журнал
• Date: 2012
• ISSN: 1027-3190
• Main Authors: Volosivets, S.S., Golubov, B.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164425
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Fourier cosine and sine transforms and generalized Lipschitz classes in the uniform metric / B.I. Golubov, S.S. Volosivets // Український математичний журнал. — 2012. — Т. 64, № 5. — С. 616-627. — Бібліогр.: 16 назв. — англ.

For functions f ∈ L¹ (ℝ+) with cosine (sine) Fourier transforms f^c (f^s) in L¹ (ℝ), we give necessary and sufficient conditions in terms of f^c (f^s) for f to belong to generalized Lipschitz classes H^ω,m and h^ω,m Conditions for the uniform convergence of the Fourier integral and for the existence...