Abstract: In consideration of the Orlicz sequence spaces,p-Amemiya function is defined.By means of real and functional analysis method,feature of p-Amemiya (1≤p≤∞) function and the characterizations over attainability of p-Amemiya norm in the Orlicz sequence spaces are discussed.A whole series of properties of p-Amemiya function are presented.Based on the conclusions,attainability of p-Amemiya norm is derived.And the intervals for p-Amemiya norm attainability are described.

Key words: Orlicz sequence space, p-Amemiya function, p-Amemiya norm, attainability