Abstract: Aiming at  the compactness problem of dual Toeplitz operators on Fock spaces with general Gaussian measures. We first defined logarithm-type complete square functions, and then by constructing a family of auxiliary functions, and using methods such as scaling and multiplication operator decompositions, we gave  necessary and sufficient conditions for the boundedness and compactness of dual Toeplitz operators on Fock spaces with general Gaussian measures. This extended the research methods of  dual Toeplitz operators on Fock spaces to the general Gaussian measure Fock spaces.

Key words: Fock space, dual Toeplitz operator, Gaussian measure, compactness, boundedness