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Weighted inequalities involving Riemann-Liouville and Hardy-type operators

Prokhorov, Dmitry V (author)
Luleå tekniska universitet
 (creator_code:org_t)
Luleå : Luleå tekniska universitet, 2003
English 16 s.
Series: Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, 1402-1544 ; 2003:38
  • Doctoral thesis (other academic/artistic)
Abstract Subject headings
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  • 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)
NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Mathematics
Matematik

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