  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.
