Multipliers for Pairs of Grand and Small Lebesgue Space for p∈(1,∞)

For a wide class of grand Lebesgue spaces, we give an exact description of the multiplier space between a couple of grand Lebesgue spaces from this class. It is shown that in this case the multiplier space for a couple of grand Lebesgue spaces is a grand Lebesgue space structurally constructed from the original spaces. A similar result is true for couples of small Lebesgue spaces.