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We obtain Gagliardo-Nirenberg interpolation inequalities of the form ‖∇u‖X ≤ C1 √ ‖u|‖Y ‖∇(2)u‖Z + C2‖u‖Y , where X,Y,Z are Orlicz spaces related to a single measure which may not satisfy the doubling condition. Some examples among homogeneous, logarithmic and exponential spaces are given.

Gagliardo-Nirenberg inequalities in weighted Orlicz spaces equipped with a nonnecessarily doubling measure