Weighted inequalities involving Riemann-Liouville and Hardy-type operators
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Necessary and sufficient conditions for the weighted boundedness and compactness of the Riemann-Liouville operators are obtained. Applications to the solvability of the Abel nonlinear integral equations and to embedding theorems of some Besov-type spaces into weighted Lebesgue spaces on the semiaxis are given. A criterion for the boundedness of the Riemann-Liouville type operator with variable limits between Lebesgue spaces on the semiaxis is given. Some Sobolev-type spaces are considered and a necessary and sufficient condition for their embedding into a Lebesgue space on the real axis is given. A new geometric mean integral operator is introduced and a necessary and sufficient condition for its mapping between Lebesgue spaces on the semiaxis is proved. The key point of the proof is to first derive a similar result for the corresponding Hardy operator. A precise characterization of Hardy type inequalities with weights for the negative indices and the indices between 0 and 1 are obtained and a duality between these cases is established.
Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2003. , 16 p.
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544 ; 2003:38
Research subject Mathematics
IdentifiersURN: urn:nbn:se:ltu:diva-26464Local ID: e5bac600-6d6c-11db-83c6-000ea68e967bOAI: oai:DiVA.org:ltu-26464DiVA: diva2:999626
Godkänd; 2003; 20061106 (haneit)2016-09-302016-09-302016-10-20Bibliographically approved