  Nonparametric density estimators are studied for $d$-dimensional, strongly
spatial mixing data which is defined on a general $N$-dimensional lattice
structure. We consider linear and nonlinear hard thresholded wavelet estimators
which are derived from a $d$-dimensional multiresolution analysis. We give
sufficient criteria for the consistency of these estimators and derive rates of
convergence in $L^{p'}$ for $p'\in [1,\infty)$. For this reason, we study
density functions which are elements of a $d$-dimensional Besov space
$B^s_{p,q}(\mathbb{R}^d)$. We also verify the analytic correctness of our
results in numerical simulations.
