Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T13:38:46.120Z Has data issue: false hasContentIssue false
  • English
  • Français

Norm inequalities of product form in weighted Lp spaces

Published online by Cambridge University Press:  14 November 2011

M. K. Kwong  and
A. Zettl
M. K. Kwong
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, U.S.A.
A. Zettl
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

The classical inequality ‖y′‖2≦K‖y‖ ‖y″‖ and its higher order analogues are extended from the Lp spaces to the weighted spaces, for appropriate w.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 89 , Issue 3-4 , 1981 , pp. 293 - 307
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Everitt, W. N.. A note on an integral inequality. Quaestiones Math. 2 (1978), 461–478.CrossRefGoogle Scholar
2Everitt, W. N.. On an extension to an integro-differential inequality of Hardy, Littlewood and Polya. Proc. Roy. Soc. Edinburgh Sect. A 69 (1972), 295–333.Google Scholar
3Everitt, W. N. and Zettl, A.. On a class of integral inequalities. J. London Math. Soc. 17 (1978), 291–303.CrossRefGoogle Scholar
4Gabushin, V. N.. Inequalities for norms of a function and its derivatives in Lp metrics. Mat. Zametki 1 (1967), 291–298.Google Scholar
5Hardy, G. H. and Littlewood, J. E.. Some integral inequalities connected with the calculus of variations. Quart. J. Math. Oxford 3 (1932), 241–252.CrossRefGoogle Scholar
6Kallman, R. R. and Rota, G. C.. On the inequality ‖f'‖2 ≦ 4 ‖f‖ ‖f’‖. Inequalities II (Shisha, O., ed.) (New York: Academic Press, 1970).Google Scholar
7Kato, T.. On an inequality of Hardy, Littlewood and Polya. Adv. in Math. 7 (1971), 217–218.CrossRefGoogle Scholar
8Kupcov, N. P.. Kolmogorov estimates for derivatives in L 2(0, ∞). Proc. Steklov Inst. Math. 138 (1975), (AMS Transl. 1977, 101–125).Google Scholar
9Kwong, M. K. and Zettl, A.. Landau's inequality pre-print.Google Scholar
10Kwong, M. K. and Zettl, A.. An extension of the Hardy–Littlewood inequality. Proc. Amer. Math. Soc. 77 (1979), 117–118.CrossRefGoogle Scholar
11Kwong, M. K. and Zettl, A.. Weighted norm inequalities of sum form involving derivatives. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 121–134.CrossRefGoogle Scholar
12Kwong, M. K. and Zettl, A.. Ramifications of Landau's inequality. Proc. Roy. Soc. Edinburgh Sect. A 86 (1981), 175–212.CrossRefGoogle Scholar
13Ljubič, Ju. I.. On inequalities between the powers of a linear operator. Trans. Amer. Math. Soc. 40 (1964), 39–84.Google Scholar
14Müller-Pfeiffer, E.. Spektraleigenschaften singulärer gewöhnlicher differentialoperatoren (Leipzig: Teubner-Texte zur Mathematik, 1977).Google Scholar
15Schönberg, I. J. and Cavaretta, A.. Solution of Landau's problem concerning higher derivatives on the half line. MRCTSR1050, Madison, Wisconsin, 1970.Google Scholar
16Hardy, G. H., Littlewood, J. E. and Polya, G.. Inequalities (Cambridge Univ. Press, 1934)Google Scholar