Martinazzi, Luca. (2015) Fractional Adams–Moser–Trudinger type inequalities. Nonlinear Analysis, 127. pp. 263278.
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Abstract
Extending several works, we prove a general Adams Moser Trudinger type inequality for the embedding of Besselpotential 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/p1dx <= 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 Lorentzspaces (i.e. (Delta) u is an element of L(P,Lq)). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cutoff 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 Qcurvature and some open problems.
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/p1dx <= 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 Lorentzspaces (i.e. (Delta) u is an element of L(P,Lq)). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cutoff 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 Qcurvature 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 
Publisher:  Elsevier 
ISSN:  0362546X 
eISSN:  18735215 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
Identification Number: 

edoc DOI:  
Last Modified:  30 Aug 2016 09:17 
Deposited On:  30 Aug 2016 09:17 
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