Explicit representations for Banach subspaces of Lizorkin distributions

S Neumayer, M Unser - Analysis and Applications, 2023 - infoscience.epfl.ch
The Lizorkin space is well suited to the study of operators like fractional Laplacians and the
Radon transform. In this paper, we show that the space is unfortunately not complemented in …

Continuity properties of the shearlet transform and the shearlet synthesis operator on the Lizorkin type spaces

F Bartolucci, S Pilipović… - Mathematische …, 2022 - Wiley Online Library
We develop a distributional framework for the shearlet transform S ψ: S 0 (R 2)→ S (S)
S_ψ:S_0\big(R^2\big)→S(S) and the shearlet synthesis operator S ψ t: S (S)→ S 0 (R 2) …