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A Remark on a Weighted Landau Inequality of Kwong and Zettl

Published online by Cambridge University Press:  20 November 2018

R. C. Brown ,
D. B. Hinton  and
M. K. Kwong
R. C. Brown
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487-0350, U.S.A. e-mail:dicbrown@ualvm.ua.edu
D. B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1300 U.S.A. e-mail:hinton @novell.math. utk.edu
M. K. Kwong
Affiliation:
Mathematics and Computer Science Division, Building 221, Argonne National Laboratory, Argonne, Illinois 60439, U.S.A., e-mail: kwong@mcs.anl.gov
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Abstract

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In this note we extend a theorem of Kwong and Zettl concerning the inequality

The Kwong-Zettl result holds for 1 ≤ p < ∞ and real numbers α, β, γ such that the conditions (i) β = (α + γ)/2, (ii) β > - 1 , and (iii) γ - 1 - p hold. Here the inequality is proved with β satisfying (i) for all α, γ except p — 1,-1 — p. In this case the inequality is false; however u is shown to satisfy the inequality

Keywords

26D1026D1526D20weighted Landau inequalities
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 34 - 41
Copyright
Copyright © Canadian Mathematical Society 1995

References

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