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The main purpose of this paper is to prove Hörmander’s $L^p$–$L^q$ boundedness of Fourier multipliers on commutative hypergroups. We carry out this objective by establishing the Paley inequality and Hausdorff–Young–Paley inequality for commutative hypergroups. We show the $L^p$–$L^q$ boundedness of the spectral multipliers for the generalised radial Laplacian by examining our results on Chébli–Trimèche hypergroups. As a consequence, we obtain embedding theorems and time asymptotics for the $L^p$–$L^q$ norms of the heat kernel for generalised radial Laplacian.

We show results on Lp-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator with Hodge boundary conditions and the Lamé system. Here, we rely on resolvent estimates recently established by Mitrea and Monniaux.

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$\boldsymbol {L}^{\boldsymbol {p}}$–$\boldsymbol {L}^{\boldsymbol {q}}$ MULTIPLIERS ON COMMUTATIVE HYPERGROUPS

Lp-Spectral Multipliers for some Elliptic Systems

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2 results

$\boldsymbol {L}^{\boldsymbol {p}}$–$\boldsymbol {L}^{\boldsymbol {q}}$ MULTIPLIERS ON COMMUTATIVE HYPERGROUPS

Lp-Spectral Multipliers for some Elliptic Systems