The Gabor Transform is also referred to as the Short Time Fourier Transform (STFT). Filtering the time-frequency content of a signal is indeed one of the main applications of Gabor multipliers. An important difference to wavelet theory is a consequence of the so-called Balian-Low principle.
To learn more about the Gabor Analysis you can read:
H. Bölcskei and F. Hlawatsch, “Oversampled modulated filter banks,”
in Gabor Analysis and Algorithms: Theory and Applications, H. G. Feichtinger
and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, ch. 9,
pp. 295–322.
H. G. Feichtinger and T. Strohmer, Eds., “Gabor analysis and algorithms:
Theory and applications,” in Applied and Numerical Harmonic Analysis.
Boston, MA: Birkhäuser, 1998.