Affine synthesis and coefficient norms for Lebesgue, Hardy and Sobolev spaces

Huy-Qui Bui, Richard S. Laugesen

The affine synthesis operator is shown to map the mixed-norm sequence space ${\ell }^1({\ell }^p)$ surjectively onto $L^p(\Rd), 1 \leq p < \infty$, assuming the Fourier transform of the…