Gagliardo-Nirenberg inequalities in weighted Orlicz spaces equipped with a nonnecessarily doubling measure
Agnieszka Kałamajska and Katarzyna Pietruska-Pałuba
Source: Bull. Belg. Math. Soc. Simon Stevin Volume 15, Number 2 (2008), 217-235.
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.
Primary Subjects: 26D10
Secondary Subjects: 46E35, 54C30, 35A25
Keywords: Gagliardo-Nirenberg inequalities; Orlicz-Sobolev spaces; nondoubling measures
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bbms/1210254820
Bulletin of the Belgian Mathematical Society - Simon Stevin
