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February 2022 An improvement of Bernstein’s inequality for functions in Orlicz spaces with smooth Fourier image
Ha Huy Bang, Vu Nhat Huy
Rocky Mountain J. Math. 52(1): 29-42 (February 2022). DOI: 10.1216/rmj.2022.52.29

Abstract

Let Φ:[0,+)[0,+] be an arbitrary Young function and K be a compact set in n having (O)-property. Then there exists a constant CK,Φ< independent of f such that

Dαf(Φ)CK,ΦsupzK|zα|fK,3

for all α+n and fK,3, where K,3={f𝒮(n):suppf^K,D(3,3,,3)f^C(n)}, fK,3=D(3,3,,3)f^, f^ is the Fourier transform of f and (Φ) is the Luxemburg norm. As an application, a new Paley–Wiener theorem is given.

Citation

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Ha Huy Bang. Vu Nhat Huy. "An improvement of Bernstein’s inequality for functions in Orlicz spaces with smooth Fourier image." Rocky Mountain J. Math. 52 (1) 29 - 42, February 2022. https://doi.org/10.1216/rmj.2022.52.29

Information

Received: 29 January 2021; Accepted: 8 May 2021; Published: February 2022
First available in Project Euclid: 19 April 2022

Digital Object Identifier: 10.1216/rmj.2022.52.29

Subjects:
Primary: 26D10 , 41A17 , 42B10 , 46E30

Keywords: Bernstein inequality , Fourier transform , generalized functions , inequalities in approximation , Orlicz spaces

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 1 • February 2022
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