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Convolution Inequalities in lp Weighted Spaces

Published online by Cambridge University Press:  20 November 2018

Nguyen Du Vi Nhan and
Dinh Thanh Duc
Nguyen Du Vi Nhan
Affiliation:
Department of Mathematics, Quy Nhon University, Binh Dinh, Vietnam e-mail: ndvynhan@gmail.com e-mail: ducdinh2002@yahoo.com
Dinh Thanh Duc
Affiliation:
Department of Mathematics, Quy Nhon University, Binh Dinh, Vietnam e-mail: ndvynhan@gmail.com e-mail: ducdinh2002@yahoo.com
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Abstract

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Various weighted ${{l}_{p}}$ -norm inequalities in convolutions are derived by a simple and general principle whose ${{l}_{2}}$ version was obtained by using the theory of reproducing kernels. Applications to the Riemann zeta function and a difference equation are also considered.

Keywords

26D1544A35inequalities for sumsconvolution

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012, pp. 355 - 367
Copyright
Copyright © Canadian Mathematical Society 2012

References

[1] Borwein, D. and Kratz, W., Weighted convolution operators on ℓ p . Canad. Math. Bull. 48(2005), 175–179. http://dx.doi.org/10.4153/CMB-2005-015-x Google Scholar
[2] Debnath, L. and Bhatta, D., Integral Transforms and Their Applications. Chapman & Hall/CRC, Boca Raton, 2007.Google Scholar
[3] Mitrinović, D. S., Pečarić, J. E. and Fink, A. M., Classic and New Inequalities in Analysis. Kluwer Academic Publishers, The Netherlands, 1993.Google Scholar
[4] Poularikas, A. D., The Transforms and Applications Handbook: Second Edition. CRC Press LLC, Boca Raton, 2000.Google Scholar
[5] Saitoh, S., Integral Transforms, Reproducing Kernels and Their Applications. Pitman Research Notes in Mathematics Series 369, Longman, Harlow, 1998.Google Scholar
[6] Saitoh, S., Various operators in Hilbert space introduced by transforms. Int. J. Appl. Math. 1(1999), 111–126.Google Scholar
[7] Saitoh, S., Tuan, V. K. and Yamamoto, M., Convolution inequalities and applications. J. Inequal. Pure Appl. Math. 4(2003), Article 50 (electronic).Google Scholar
[8] Liu, Xiao-Hua, On the inverses of Hölder's inequalities. Math. Practice Theory 1990, 84–88.Google Scholar