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Volume 1, Issue 1, 2000

Article 7

http://jipam.vu.edu.au/v1n1/018_99.html

REVERSE WEIGHTED Lp –NORM INEQUALITIES IN CONVOLUTIONS

SABUROU SAITOH, VU KIM TUÂN  
AND MASAHIRO YAMAMOTO

DEPARTMENT OF MATHEMATICS,
FACULTY OF ENGINEERING,
GUNMA UNIVERSITY,
KIRYU 376-8515, JAPAN
EMail: ssaitoh@eg.gunma-u.ac.jp

DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE,
FACULTY OF SCIENCE,
KUWAIT UNIVERSITY,
P.O. BOX 5969, SAFAT 13060, KUWAIT
EMail: vu@sci.kuniv.edu.kw

DEPARTMENT OF MATHEMATICAL SCIENCES,
THE UNIVERSITY OF TOKYO,
3-8-1 KOMABA, TOKYO 153-8914, JAPAN
EMail: myama@ms.u-tokyo.ac.jp

Received and accepted 14 November, 1999.
Communicated by: J.E. Pecaric.

ABSTRACT. Various weighted Lp (p > 1)–norm inequalities in convolutions were derived by using Hölder’s inequality. Therefore, by using reverse Hölder inequalities one can obtain reverse weighted Lp –norm inequalities. These inequalities are important in studying stability of some inverse problems.
Key words:
Convolution, weighted Lp inequality, reverse Hölder inequality, inverse problems, Green’s function, integral transform, stability.

2000 Mathematics Subject Classification: 44A35, 26D20.
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Other papers in this issue

Volume 1, Number 1, 2000
http://jipam.vu.edu.au/v1n1/

1.

Power-monotone sequences and Fourier series with positive coefficients

L. Leindler

 2.

On Hadamard's Inequality on a Disk

S.S. Dragomir
3.

A Steffensen Type Inequality

Hillel Gauchman

 4.

Generalized Abstracted Mean Values

Feng Qi
5.

An Inequality for Linear Positive Functionals

Bogdan Gavrea and Ioan Gavrea

 6.

Inequalities for Planar Convex Sets

Paul R. Scott and Poh Wah Awyong
7.

Reverse Weighted Lp - Norm Inequalities in Convolutions

Saburou Saitoh, Vu Kim Tuan and Masahiro Yamamoto

 8.

Existence and Local Uniqueness for Nonlinear Lidstone Boundary Value Problems

Jeffrey Ehme and Johnny Henderson
9.

On Hadamard's Inequality for the Convex Mappings Defined on a Convex Domain in the Space

Bogdan Gavrea

 10.

Weighted Modular Inequalities for Hardy-Type Operators on Monotone Functions

Hans P. Heinig and Qinsheng Lai
 

Editors

R.P. Agarwal
G. Anastassiou
T. Ando
H. Araki
A.G. Babenko
D. Bainov
N.S. Barnett
H. Bor
J. Borwein
P.S. Bullen
P. Cerone
S.H. Cheng
L. Debnath
S.S. Dragomir
N. Elezovic
A.M. Fink
A. Fiorenza
T. Furuta
L. Gajek
H. Gauchman
C. Giordano
F. Hansen
D. Hinton
A. Laforgia
L. Leindler
C.-K. Li
L. Losonczi 
A. Lupas
R. Mathias
T. Mills
G.V. Milovanovic
R.N. Mohapatra
B. Mond
M.Z. Nashed
C.P. Niculescu
I. Olkin
B. Opic
B. Pachpatte
Z. Pales
C.E.M. Pearce
J. Pecaric
L.-E. Persson
L. Pick
I. Pressman
S. Puntanen
F. Qi
A.G. Ramm
T.M. Rassias
A. Rubinov
S. Saitoh
J. Sandor
S.P. Singh
A. Sofo
H.M. Srivastava
K.B. Stolarsky
G.P.H. Styan
L. Toth
R. Verma
F. Zhang

© 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

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