Fractional Adams–Moser–Trudinger type inequalities

Martinazzi, Luca. (2015) Fractional Adams–Moser–Trudinger type inequalities. Nonlinear Analysis, 127. pp. 263-278.

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Official URL: http://edoc.unibas.ch/43978/

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Extending several works, we prove a general Adams Moser Trudinger type inequality for the embedding of Bessel-potential spaces (r2) into Orlicz spaces for an arbitrary domain,r2 with finite measure. In particular we prove
sup (u is an element of Hn/p,p (Omega), parallel to(-Delta)n/2p u parallel to LP(Omega)<= 1) integral Omega (E alpha n,p broken vertical bar u broken vertical bar p/p-1dx <= Cn,p broken vertical bar Omega broken vertical bar,)
for a positive constant amp whose sharpness we also prove. We further extend this result to the case of Lorentz-spaces (i.e. (-Delta) u is an element of L-(P,L-q)). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cut-off procedures to reduce the fractional results to the sharp estimate on the Riesz potential proven by Adams and its generalization proven by Xiao and Zhai. We also discuss an application to the problem of prescribing the Q-curvature and some open problems.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Analysis (Martinazzi)
UniBasel Contributors:Martinazzi, Luca
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:30 Aug 2016 09:17
Deposited On:30 Aug 2016 09:17

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