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

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-23
Published: Jan 29, 2024
Cite as:
Pebrudal Zanu, Wono Setya Budhi, Yudi Soeharyadi, The Exact Norm of Modified Hardy Operator in Power-Weighted Lebesgue Spaces, Int. J. Anal. Appl., 22 (2024), 23.

Main Article Content

Pebrudal Zanu, Wono Setya Budhi, Yudi Soeharyadi

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.

Article Details

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.