Novel Generalized Fractional Calderon–Zygmund Operators with ´Rough Spatial Kernels and Applications to Two-Dimensional Delayed Parabolic Equations

Authors

  • Afzal Waqar
  • Mujahid Abbas Department of Mechanical Engineering Sciences, Faculty of Engineering and the Built Environment, Doornfontein Campus, University of Johannesburg, South Africa
  • Jorge E. Macias-Diaz
  • Ernesto Urenda-Cazares
  • Mehreen Shehzadi Khan Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
  • Hafeez Sultana Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
  • Omniat Omer Yousif Karrar Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
  • Leema Aliyarukunju Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
  • Daniel Breaz Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
  • Luminita-Ioana Cotırla Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.7489

Keywords:

Herz spaces, Calderon–Zygmund operators, Spatial roughness, Well-posedness

Abstract

In this paper, we investigate the boundedness properties of a novel class of generalized fractional Calderón--Zygmund operators with spatially rough kernels. By employing refined analytical techniques together with appropriate structural assumptions, we derive sharp estimates and recover several known results as special cases. As an application, these results are applied to study the regularity and well-posedness of a nonlinear delayed parabolic equation.

References

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Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Nonlinear Analysis

License

Copyright (c) 2026 Afzal Waqar, Mujahid Abbas, Jorge E. Macias-Diaz, Ernesto Urenda-Cazares, Mehreen Shehzadi Khan, Hafeez Sultana, Omniat Omer Yousif Karrar, Leema Aliyarukunju , Daniel Breaz, Luminita-Ioana Cotırla

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How to Cite

Novel Generalized Fractional Calderon–Zygmund Operators with ´Rough Spatial Kernels and Applications to Two-Dimensional Delayed Parabolic Equations. (2026). European Journal of Pure and Applied Mathematics, 19(2), 7489. https://doi.org/10.29020/nybg.ejpam.v19i2.7489