{E : Type u_1} →
  {F : Type u_2} →
    [inst : NormedAddCommGroup E] →
      [inst_1 : MeasurableSpace E] →
        [inst_2 : BorelSpace E] →
          [inst_3 : NormedAddCommGroup F] →
            [InnerProductSpace ℂ F] →
              [CompleteSpace F] →
                [inst_6 : InnerProductSpace ℝ E] →
                  [inst_7 : FiniteDimensional ℝ E] →
                    FourierTransform ↥(MeasureTheory.Lp F 2 MeasureTheory.volume)
                      ↥(MeasureTheory.Lp F 2 MeasureTheory.volume)