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Weighted inequaliti...
Weighted inequalities involving Riemann-Liouville and Hardy-type operators
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- Prokhorov, Dmitry V (författare)
- Luleå tekniska universitet
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(creator_code:org_t)
- Luleå : Luleå tekniska universitet, 2003
- Engelska 16 s.
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Serie: Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, 1402-1544 ; 2003:38
- Relaterad länk:
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https://urn.kb.se/re...
Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Mathematics
- Matematik
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