Publications Repository - Gdańsk University of Technology

We construct Parseval wavelet frames in L 2 (M) for a general Riemannian manifold M and we show the existence of wavelet unconditional frames in L p (M) for 1 < p < ∞. This is made possible thanks to smooth orthogonal projection decomposition of the identity operator on L 2 (M), which was recently proven by Bownik et al. (Potential Anal 54:41–94, 2021). We also show a characterization of Triebel–Lizorkin F sp,q (M) and Besov B sp,q (M) spaces on compact manifolds in terms of magnitudes of coefficients of Parseval wavelet frames. We achieve this by showing that Hestenes operators are bounded on F sp,q (M) and B sp,q (M) spaces on manifolds M with bounded geometry.

Authors

• prof Marcin Bownik,
• dr hab. Karol Dziedziul link open in new tab ,
• prof. dr hab. Anna Kamont link open in new tab