Uncertainty Principles as Embeddings of Modulation Spaces
A class of new uncertainty principles is derived in the form of embeddings of Fourier–Lebesgue spaces into modulation spaces. These embeddings provide practical, sufficient conditions for a function to belong to a modulation space. Counterexamples based on the properties of Gabor expansions demonstrate that the embeddings are optimal.
Galperin, Y. V. and Karlheinz Gröchenig. "Uncertainty Principles as Embeddings of Modulation Spaces." Journal of Mathematical Analysis and Applications 274.1 (2002): 181-202.