Subsets of F_p^n without three term arithmetic progressions have several large Fourier coefficients

Suppose that f : F_p^n -> [0,1] has expected value t in [p^(-n/9),1] (so, the density t can be quite low!). Furthermore, suppose that support(f) has no three-term arithmetic progressions. Then, we develop non-trivial lower bounds for f_j, which is the jth largest Fourier coefficient of f. This result is similar in spirit to that appearing in an earlier paper [1] by the author; however, in that paper the focus was on the small'' Fourier coefficients, whereas here the focus is on the large’’ Fourier coefficients. Furthermore, the proof in the present paper requires much more sophisticated arguments than those of that other paper.