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• Author or Editor: Djemaïa Bensikaddour
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# Regularity of solutions of Poisson’s equation in multiplier spaces

Authors: Djemaïa Bensikaddour, Sadek Gala and Amina Lahmar-Benbernou

## Abstract

The most important result stated in this paper is to show that the solutions of the Poisson equation −Δu = f, where f

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{M}$$ \end{document}
(Ḣ1(ℝd) → (Ḣ−1(ℝd)) is a complex-valued distribution on ℝd, satisfy the regularity property D k u
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{M}$$ \end{document}
(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.

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