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The K-functional of certain pairs of rearrangement invariant spaces

Let X, Y be rearrangement invariant spaces and let M = M(Y, X) be the space of all multipliers of Y into X. It is shown that if X = YM and some technical conditions are satisfied, then the K-functional K(t, f, X, Y) is equivalent to the expression where ψ is the inverse of the fundamental function ϕM of M, defined by