  We discuss generalizations of Rubio de Francia's inequality for
Triebel--Lizorkin and Besov spaces, continuing the research from [5]. Two
versions of Rubio de Francia's operator are discussed: it is shown that a
rotation factor is needed for the boundedness of the operator in some smooth
spaces while it is not essential in other spaces. We study the operators on
some "end" spaces of the Triebel--Lizorkin scale and then use usual
interpolation methods.
