ABSTRACT
W e shal l now show that equalities (6.9.3) and (6.9.4) are also true. I n accordance w i t h E x a m p l e 1.8.4, (6.4.3) and (6.4.4) we ob ta in
^ T ( ^ ) = rxT{(p) = T ( r _ x £ ) = T ( e ^ V ) = e^fiip)
110 and
¿M~T(<p) = (e^T)^) = T(e^ip) = T(r^p) = T{TXV>) = r _ B T ( y ) ) . T h e consequence of this reason is easily seen because of R e m a r k 6.1.1. •
6.10. Fourier transforms of integrable distributions
P u t Ex(x) ~ ( 2 7 r ) - t A - n e - i l A | 2
(compare Sect ion 4.3). Le t T be in VfLl, then Tx(x) = (T*Ex)(x)=T(Ex(x--))
is a regular iza t ion of T (see Sect ion 5.2). T h e first theorem of this section gives us some general izat ion of the Riemann-Lebesgue l emma.
