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Global behavior of integral transforms

Journal of Inequalities and Applications volume 2006, Article number: 61980 (2006) Cite this article

Abstract

We obtain global estimates for various integral transforms of positive differentiable functions that satisfy inequalities of the type, for.

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References

  1. Berndt R: A formula for the Fourier transform of certain odd differentiable functions. Journal of Mathematical Analysis and Applications 2003,285(2):349–355. 10.1016/S0022-247X(03)00243-9

    Article  MATH  MathSciNet  Google Scholar 

  2. Berndt R: Singular integrals with new singularities, Dissertation. University of Minnesota, Minnesota; 2003.

    Google Scholar 

  3. Estrada R: Regularization of distributions. International Journal of Mathematics and Mathematical Sciences 1998,21(4):625–636. 10.1155/S016117129800088X

    Article  MATH  MathSciNet  Google Scholar 

  4. Estrada R, Kanwal RP: A Distributional Approach to Asymptotics. Theory and Applications, Birkhäuser Advanced Texts: Basel Textbooks. 2nd edition. Birkhäuser Boston, Massachusetts; 2002:xvi+451.

    Book  Google Scholar 

  5. Kanwal RP: Generalized Functions. Theory and Technique. 2nd edition. Birkhäuser Boston, Massachusetts; 1998:xii+462.

    MATH  Google Scholar 

  6. Seneta E: Regularly Varying Functions, Lecture Notes in Mathematics. Volume 508. Springer, Berlin; 1976:v+112.

    Book  Google Scholar 

  7. Soni K, Soni RP: Slowly varying functions and asymptotic behavior of a class of integral transforms. I. Journal of Mathematical Analysis and Applications 1975,49(1):166–179. 10.1016/0022-247X(75)90168-7

    Article  MATH  MathSciNet  Google Scholar 

  8. Soni K, Soni RP: Slowly varying functions and asymptotic behavior of a class of integral transforms. II. Journal of Mathematical Analysis and Applications 1975,49(1):477–495.

    Article  MATH  MathSciNet  Google Scholar 

  9. Soni K, Soni RP: Slowly varying functions and asymptotic behavior of a class of integral transforms. III. Journal of Mathematical Analysis and Applications 1975,49(3):612–628. 10.1016/0022-247X(75)90201-2

    Article  MATH  MathSciNet  Google Scholar 

  10. Trèves F: Topological Vector Spaces, Distributions and Kernels. Academic Press, New York; 1967:xvi+624.

    MATH  Google Scholar 

  11. Zemanian AH: Distribution Theory and Transform Analysis. An Introduction to Generalized Functions, with Applications. 2nd edition. Dover, New York; 1987:xii+371.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematics Department, Louisiana State University, Baton Rouge, LA, 70803, USA

    Jasson Vindas & Ricardo Estrada

Authors
  1. Jasson Vindas
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  2. Ricardo Estrada
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Correspondence to Ricardo Estrada.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Vindas, J., Estrada, R. Global behavior of integral transforms. J Inequal Appl 2006, 61980 (2006). https://doi.org/10.1155/JIA/2006/61980

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  • DOI: https://doi.org/10.1155/JIA/2006/61980

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