Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition

In this paper we extend the duality ■ to generalized Campanato spaces with variable growth condition Lp,φ（Rd） instead of BMO（Rd）.We also extend the characterization of ■by Uchiyama （1978） to ■.Moreover,using this characLterization,we prove the boundedness of singular and fractional integral operators on ■.The function space Lp,φ（Rd） treated in this paper covers the case that it is coincide with Lipα on one area,with BMO on another area and with the Morrey space on the other area,for example.