Periodica Mathematica Hungarica

, Volume 57, Issue 1, pp 1–22 | Cite as

Regularity of solutions of Poisson’s equation in multiplier spaces

  • Djemaïa Bensikaddour
  • Sadek Gala
  • Amina Lahmar-Benbernou


The most important result stated in this paper is to show that the solutions of the Poisson equation −Δu = f, where f\( \mathcal{M} \)(Ḣ1(ℝ d ) → (Ḣ−1(ℝ d )) is a complex-valued distribution on ℝ d , satisfy the regularity property D k u\( \mathcal{M} \)(Ḣ1 → Ḣ−1) for all k, |k| = 2. The regularity of this equation is well studied by Maz’ya and Verbitsky [12] in the case where f belongs to the class of positive Borel measures.

Key words and phrases

Poisson equation regularity of solutions multiplier space 

Mathematics subject classification numbers

35F05 42B15 42B35 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Djemaïa Bensikaddour
    • 1
  • Sadek Gala
    • 1
  • Amina Lahmar-Benbernou
    • 1
  1. 1.Department of MathematicsUniversity of MostaganemMostaganemAlgeria

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