Maintaining constant gain through impedance coupling
This schematic ought to be shown in a more familiar LC filter arrangement to show the response more clearly as I have a done below.



The centre shunt coil independently controls the 1st pole when its L impedance is lower.  While the outer loop of series L's and shunt C's controls the other pole.  Q is controlled mainly by source impedance ( such as a current source with load R.) while load impedance ratio affects slope of skirts.

Rather than call it Inductive coupling, it is more accurately impedance ratios of series/shunt elements that control the response.  

A simple FM filter is shown that I quickly designed. (not optimal)



Note above the FM filter requires both series L and shunt caps to be the same to tune the upper pole for equal peaks and the centre shunt L tunes the 1st pole is 1/4 of the series L elements.

Your title of this question is misleading.

None of this filter arrangement provides "Maintaining constant gain through impedance coupling".  This is done by AGC bias control in the preceding active stage.  You might want to edit your question to reflect the details in the question such as LC double tuned filter without mutual coupling.