Journal of the
Korean Mathematical Society JKMS

This paper deals with Littlewood-Paley type estimates of the Besov
spaces $\Ba{p}{q}$ on the $d$-dimensional unit cube for $0 by two certain classes.
These classes are including biorthogonal wavelet systems or dual
multiscale systems but not necessarily obtained as the dilates or translates
of certain fixed functions.
The main assumptions are local supports of both classes, sufficient smoothness
for one class, and sufficiently many vanishing moments for the other class.
With these estimates, we characterize the Besov spaces by
coefficient norms of decompositions with respect to
biorthogonal wavelet systems on the cube.

Keywords: Besov spaces, Littlewood-Paley estimates, wavelet decompositions, biorthogonal wavelets

MSC numbers: 41A17, 41A30, 42C15, 43A32, 46A45