Journal
INDIANA UNIVERSITY MATHEMATICS JOURNAL
Volume 55, Issue 6, Pages 1951-1974Publisher
INDIANA UNIV MATH JOURNAL
DOI: 10.1512/iumj.2006.55.2743
Keywords
Trudinger-Moser inequality; Gagliadro-Nirenberg inequality; Sobolev inequality; rearrangement; average function; Riesz potential; fractional integral
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We will consider a Trudinger-Moser inequality for the critical Sobolev space H-n/p,H-p (R-n) with the fractional derivatives in R-n and obtain an upper bound of the best constant of such an inequality. Moreover, by changing normalization from the homogeneous norm to the inhomogeneous one, we will give the best constant in the Hilbert space H-n/2,H-2 (R-n). As an application, we will obtain some lower bound of the best constant of a Gagliardo-Nirenberg inequality.
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