Abstract
We obtain Gagliardo-Nirenberg interpolation inequalities of the form $\| \nabla u\|_{X}\leq C_1\sqrt{\| u|\|_{Y}\|\nabla^{(2)}u\|_Z}+C_2\| u\|_Y$, 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.
Citation
Agnieszka Kałamajska. Katarzyna Pietruska-Pałuba. "Gagliardo-Nirenberg inequalities in weighted Orlicz spaces equipped with a nonnecessarily doubling measure." Bull. Belg. Math. Soc. Simon Stevin 15 (2) 217 - 235, May 2008. https://doi.org/10.36045/bbms/1210254820
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