Parseval Wavelet Frames on Riemannian Manifold

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