Gagliardo-Nirenberg inequalities in weighted Orlicz spaces equipped with a nonnecessarily doubling measure
Kałamajska, Agnieszka ; Pietruska-Pałuba, Katarzyna
Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, p. 217-235 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  Gagliardo-Nirenberg inequalities,  Orlicz-Sobolev spaces,  nondoubling measures,  26D10,  46E35,  54C30,  35A25 
@article{1210254820,
     author = {Ka\l amajska, Agnieszka and Pietruska-Pa\l uba, Katarzyna},
     title = {Gagliardo-Nirenberg inequalities
in weighted Orlicz spaces equipped with a nonnecessarily
doubling measure},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {15},
     number = {1},
     year = {2008},
     pages = { 217-235},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1210254820}
}

Kałamajska, Agnieszka; Pietruska-Pałuba, Katarzyna. Gagliardo-Nirenberg inequalities
in weighted Orlicz spaces equipped with a nonnecessarily
doubling measure. Bull. Belg. Math. Soc. Simon Stevin, Tome 15 (2008) no. 1, pp.  217-235. http://gdmltest.u-ga.fr/item/1210254820/