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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:[email protected]
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: [email protected]
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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

1. Brown, R. C. and Hinton, D. B., Sufficient conditions for weighted inequalities of sum form, J. Math. Anal. Appl. 123(1985), 563–578.Google Scholar
2. Brown, R. C., Interpolation inequalities with power weights for functions of one variable, J. Math. Anal. Appl. 172(1993), 233–240.Google Scholar
3. Gabushin, V. N., Inequalities for norms of a function and its derivatives in Lp metrics, Mat. Zametki 1(1967), 291–298.Google Scholar
4. De Guzman, M., Differentiation of Integrals in 葷n , Lecture Notes in Math. 481, Springer-Verlag, Berlin, 1975.Google Scholar
5. Kwong, M. K. and Zettl, A., Norm inequalities of product form in weighted LP spaces, Proc. Roy. Soc. Edinburgh Sect. A 89(1981), 293–307.Google Scholar
6. Opic, B. and Kufner, A., Hardy-type Inequalities, Longman Sci. Tech., Harlow, Essex, United Kingdom, 1990.Google Scholar