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Convolution Inequalities in lp Weighted Spaces

  • Nguyen Du Vi Nhan (a1) and Dinh Thanh Duc (a1)
Abstract

Various weighted lp -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.

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References
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[1] Borwein, D. and Kratz, W., Weighted convolution operators on p . Canad. Math. Bull. 48(2005), 175179. http://dx.doi.org/10.4153/CMB-2005-015-x
[2] Debnath, L. and Bhatta, D., Integral Transforms and Their Applications. Chapman & Hall/CRC, Boca Raton, 2007.
[3] Mitrinović, D. S., Pečarić, J. E. and Fink, A. M., Classic and New Inequalities in Analysis. Kluwer Academic Publishers, The Netherlands, 1993.
[4] Poularikas, A. D., The Transforms and Applications Handbook: Second Edition. CRC Press LLC, Boca Raton, 2000.
[5] Saitoh, S., Integral Transforms, Reproducing Kernels and Their Applications. Pitman Research Notes in Mathematics Series 369, Longman, Harlow, 1998.
[6] Saitoh, S., Various operators in Hilbert space introduced by transforms. Int. J. Appl. Math. 1(1999), 111126.
[7] Saitoh, S., Tuan, V. K. and Yamamoto, M., Convolution inequalities and applications. J. Inequal. Pure Appl. Math. 4(2003), Article 50 (electronic).
[8] Liu, Xiao-Hua, On the inverses of Hölder's inequalities. Math. Practice Theory 1990, 8488.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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