Adams inequalities on measure spaces

Details Adams inequalities on measure spaces Adams inequalities on measure spaces

2009-06-29

arxiv.org/abs/0906.5103v4

Mathematics

Analysis of PDEs

To appear in Advances in Mathematics. 54 Pages, minor changes and corrections in v2 (page 1, proof of Corollary 13, some typos

Scientific paper

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz potential. In this paper we extend and improve Adams' results to functions defined on arbitrary measure spaces with finite measure. The Riesz fractional integral is replaced by general integral operators, whose kernels satisfy suitable and explicit growth conditions, given in terms of their distribution functions; natural conditions for sharpness are also given. Most of the known results about Moser-Trudinger inequalities can be easily adapted to our unified scheme. We give some new applications of our theorems, including: sharp higher order Moser-Trudinger trace inequalities, sharp Adams/Moser-Trudinger inequalities for general elliptic differential operators (scalar and vector-valued), for sums of weighted potentials, and for operators in the CR setting.

Affiliated with

Also associated with

No associations

Rating

Adams inequalities on measure spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Adams inequalities on measure spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Adams inequalities on measure spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246964