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Gabor meets Littlewood-Paley: Gabor expansions in L p ( ℝ d )

Karlheinz Gröchenig;  Christopher Heil — 2001

Studia Mathematica

It is known that Gabor expansions do not converge unconditionally in L p and that L p cannot be characterized in terms of the magnitudes of Gabor coefficients. By using a combination of Littlewood-Paley and Gabor theory, we show that L p can nevertheless be characterized in terms of Gabor expansions, and that the partial sums of Gabor expansions converge in L p -norm.

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