  In this paper we study $p$-order methods for unconstrained minimization of
convex functions that are $p$-times differentiable ($p\geq 2$) with
$\nu$-H\"{o}lder continuous $p$th derivatives. We propose tensor schemes with
and without acceleration. For the schemes without acceleration, we establish
iteration complexity bounds of
$\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$ for reducing the functional
residual below a given $\epsilon\in (0,1)$. Assuming that $\nu$ is known, we
obtain an improved complexity bound of
$\mathcal{O}\left(\epsilon^{-1/(p+\nu)}\right)$ for the corresponding
accelerated scheme. For the case in which $\nu$ is unknown, we present a
universal accelerated tensor scheme with iteration complexity of
$\mathcal{O}\left(\epsilon^{-p/[(p+1)(p+\nu-1)]}\right)$. A lower complexity
bound of $\mathcal{O}\left(\epsilon^{-2/[3(p+\nu)-2]}\right)$ is also obtained
for this problem class.
