Multivariate Bernstein inequalities for entire functions of exponential type in Lp(Rn)(0<p<1)

In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103, 1990 ), the authors prove that the classical Bernstein inequality also holds for 0 < p ≤ 1 . We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener t...

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Bibliographic Details
Published in:Journal of inequalities and applications 2019-08, Vol.2019 (1)
Main Authors: Bang, Ha Huy, Huy, Vu Nhat, Rim, Kyung Soo
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Mathematics
Mathematics and Statistics
Online Access:Get full text
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Summary:In (Rahman and Schmeisser in Trans. Amer. Math. Soc. 320: 91–103, 1990 ), the authors prove that the classical Bernstein inequality also holds for 0 < p ≤ 1 . We extend their result for a differential operator induced by polynomials and find the several equivalent conditions to the Paley–Wiener theorem. As applications of the results, we also derive the Paley–Wiener type theorems for some special compact sets generated by number sequences, generated by polynomial, convex compact sets, in which we show that the Bernstein type inequalities have concrete upper bounds.
ISSN:1029-242X
DOI:10.1186/s13660-019-2167-7