TEMPERED DISTRIBUTIONS AND FOURIER TRANSFORMS

Since i¿(-, •) is smooth i n Q, therefore u(-,t) does not converge to / as t —» 0-fi n L ° ° ( R n ) , i f we put / = H i n (6.17.11), where i f denotes the Heaviside funct ion. It means that the above theorem is not true, when p = oo.