  We consider the problem of estimating the density of observations taking
values in classical or nonclassical spaces such as manifolds and more general
metric spaces. Our setting is quite general but also sufficiently rich in
allowing the development of smooth functional calculus with well localized
spectral kernels, Besov regularity spaces, and wavelet type systems. Kernel and
both linear and nonlinear wavelet density estimators are introduced and
studied. Convergence rates for these estimators are established, which are
analogous to the existing results in the classical setting of real-valued
variables.
