In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. 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. © 2011 Elsevier Inc.

Fontana, L., Morpurgo, C. (2011). Adams inequalities on measure spaces. ADVANCES IN MATHEMATICS, 226(6), 5066-5119 [10.1016/j.aim.2011.01.003].

Adams inequalities on measure spaces

FONTANA, LUIGI;
2011

Abstract

In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of Rn. 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. © 2011 Elsevier Inc.
Articolo in rivista - Articolo scientifico
Exponential inequalities, Moser - Trudinger, limit cases of Sobolev imbeddings.
English
2011
226
6
5066
5119
open
Fontana, L., Morpurgo, C. (2011). Adams inequalities on measure spaces. ADVANCES IN MATHEMATICS, 226(6), 5066-5119 [10.1016/j.aim.2011.01.003].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/21162
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