Convolution, Reciprocity, and Adjointness
Luis Manuel Braga de Costa Campos · 2014
If one function is bounded and integrable (7.14a) and the other function is absolutely integrable (7.14b), projective inequality (7.8b) holds (7.14c): f g f g f x g x x f x g x x f x g x ∈ ∩ ∈ [ ] = ( ) ( ) ≤ ( ) ( ) ≤ ( ) ( )∞ ∫ ∫L E L, : , max1 d d dx f g a (7.14a-c) If f ∈ Lp, g ∈ Lq then p = 2 = q in (7.11a and b) and p = ∞, q = 1 in (7.14a through c), so that in both cases (7.15c) holds.