International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

The Exact Norm of Modified Hardy Operator in Power-Weighted Lebesgue Spaces

  • Pebrudal Zanu*
  • Wono Setya Budhi
  • Yudi Soeharyadi

    * Corresponding author

    Abstract

    We consider the necessary and sufficient condition for boundedness of modified Hardy operators from a power-weighted Lebesgue space to another. We also compute the exact norm of modified n-dimensional Hardy operators from those spaces.

    How to Cite

    P. Zanu, W. S. Budhi, Y. Soeharyadi, The Exact Norm of Modified Hardy Operator in Power-Weighted Lebesgue Spaces, Int. J. Anal. Appl. 22 (2024), 23. https://doi.org/10.28924/2291-8639-22-2024-23

    BibTeX
    @article{Zanu2024,
      author  = {Zanu, Pebrudal and Budhi, Wono Setya and Soeharyadi, Yudi},
      title   = {The Exact Norm of Modified Hardy Operator in Power-Weighted Lebesgue Spaces},
      journal = {Int. J. Anal. Appl.},
      volume  = {22},
      year    = {2024},
      pages   = {23},
      doi     = {10.28924/2291-8639-22-2024-23}
    }

    References

    • [1] B. Muckenhoupt, R.L. Wheeden, Weighted Norm Inequalities for Singular and Fractional Integrals, Trans. Amer. Math. Soc. 161 (1971), 249–258.
    • [2] E.M. Stein, Singular Integral and Differentiability Properties of Functions, Vol. 2, Princeton University Press, Princeton, 1973.
    • [3] G.A. Bliss, An Integral Inequality, J. London Math. Soc. s1-5 (1930), 40–46. https://doi.org/10.1112/jlms/s1-5.1.40.
    • [4] G.H. Hardy, Note on Hilbert Theorem, Math. Z. 6 (1920), 314–317.
    • [5] G.H. Hardy, J.E. Littlewood, G. Pólya, Inequalities, 2nd ed. Cambridge University Press, Cambridge, 1952.
    • [6] N. Karapetiants, S. Samko, Equations with involutive operators, Springer, New York, 2012. https://doi.org/10.1007/978-1-4612-0183-0.
    • [7] N. Samko, Integral Operators Commuting With Dilations and Rotations in Generalized Morrey-type Spaces, Math. Methods Appl. Sci. 43 (2020), 9416–9434. https://doi.org/10.1002/mma.6279.