Characterization of L-p(R-n) using Gabor frames

We characterize L-P norms of functions on R-n for 1 < p < infinity in terms of their Gabor coefficients. Moreover; we use the Carleson-Hunt theorem to show that the Gabor expansions of L-p functions converge to the functions almost everywhere and in L-p for 1 < p < infinity. In L-1 we prove an analo gous result: the Gabor expansions converge to the functions almost everywhe re and in L-1 in a certain Cesaro sense. Consequently, we are able to estab lish that a large class of Gabor families generate Banach frames for L-p(R- n) when 1 less than or equal to p < <infinity>.