Bases of wavelets and linear operators in anisotropic Lizorkin-Triebel spaces (Q1363982)

The authors construct unconditional wavelet bases in the anisotropic Lizorkin-Triebel spaces \(F^{(s)}_{pq}\) on \(\mathbb{R}^n\). With the aid of these bases they establish continuity of the anisotropic Calderón-Zygmund operators and anisotropic pseudo-differential operators, acting in \(F^{(s)}_{pq}\). As a consequence, certain refinements are obtained for the relevant results in the isotropic case, and applications to some classical operators (heat operator, the Hilbert transform) are given.