Lebesgue-Fourier algebra of a hypergroup

Let $\mathcal{L}A(H)$ be the Lebesgue-Fourier space of a hypergroup $H$ considered as a Banach space on $H$. In addition $\mathcal{L}A(H)$ is a Banach algebra with the multiplication inherited from $L^1(H)$. Moreover If $H$ is a regular Fourier hypergroup, $\mathcal{L}A(H)$ is a Banach algebra with pointwise multiplication. We study the amenability and character amenability of these two Banach algebras.