Sharp value for the norm of composition and multiplicative operators   between two different Grand Lebesgue spaces
  We calculate in this paper the norm of composition, multiplicative and product operator, generated by multiplicative and measurable argument transformation between two different ordinary Lebesgue-Riesz and Grand Lebesgue spaces.   We set ourselves the aim to obtain the exact expression for the norm of the considered operators by means of building of appropriate examples. 
E.Ostrovsky, L.Sirota
math.FA