Continuous wavelet transform on Triebel-Lizorkin spaces

The continuous wavelet transform in higher dimensions is used to prove the regularity of weak solutions u is an element of Lp(Rn) under Qu = f where f belongs to the Triebel-Lizorkin space Fp r,q(Rn) where 1 < p, q < infinity, 0 < r < 1, and where Q = n-ary sumation |beta|<= m c beta partial differential beta is a linear partial differential operator of order m > 0 with positive constant coefficients c beta.