Adams inequalities on measure spaces

By Luigi Fontana, Carlo Morpurgo. 2009

48 citations recorded by the source corpus.

Abstract 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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e4312ed766ddaf7dae53f5a173ea9b1a0ce9ab2e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

An Improved Geometric Inequality via Vanishing Moments, with Applications to Singular Liouville Equations (2012, background): “In presence of singularities, namely when a weight h̃ as in (5) multiplies the exponential term, a modified sharp Moser-Trudinger inequality was derived in [20] and [70] (see also [18], or also [28], [40] for exensions to general settings), and takes the form (9) log ˆ”
A new approach to sharp Moser–Trudinger and Adams type inequalities: A rearrangement-free argument (2013, methodology): “We also refer the reader to the sharp Moser inequality with mean value zero by Chang and Yang [11], Lu and Yang [43], Leckband [34], sharp Moser–Trudinger trace inequalities and sharp Moser–Trudinger inequalities without boundary conditions by Cianchi [12,13], the sharp Moser–Trudinger type inequali”
Adams' Inequality with the Exact Growth Condition in ℝ4 (2014, background): “Morpurgo [18] for a generalization of Adams’ result to functions defined on arbitrary measure spaces.”
Fractional Adams–Moser–Trudinger type inequalities (2015, methodology): “For further extensions we refer to the work of Fontana and Morpurgo [17].”
Sharp Moser-Trudinger inequality on the Heisenberg group at the critical case and applications ✩ (2012, background): “The explicit formula in Theorem 1.2 about the extremal functions for the sharp Hardy–Littlewood–Sobolev inequality (1.3) is consistent with Branson, Fontana and Morpurgo's natural guess initially made in their work [14] where among other things, important progress has been made on sharp Onfri–Beckne”
Sharp singular Adams inequalities in high order Sobolev spaces (2011, background): “It can also be deduced from a general result in [23] by verifying our weight satisfies the condition in [23].”