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- Abdikalikova, Zamira, et al.
(författare)
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Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1
- 2011
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Ingår i: Czechoslovak Mathematical Journal. - : Institute of Mathematics, Czech Academy of Sciences. - 0011-4642 .- 1572-9141. ; 61:1, s. 7-26
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Tidskriftsartikel (refereegranskat)abstract
- We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n
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| 2. |
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| 3. |
- Arendarenko, Larissa, et al.
(författare)
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On the boundedness of some classes of integral operators in weighted Lebesgue spaces
- 2012
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Ingår i: Eurasian Mathematical Journal. - 2077-9879. ; 3:1, s. 5-17
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Tidskriftsartikel (refereegranskat)abstract
- Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case 1 < q < p < ∞ is considered and the involved kernels satisfy conditions, which are less restrictive than the usual Oinarov condition.
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| 4. |
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| 5. |
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| 6. |
- Maligranda, Lech, et al.
(författare)
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On Hardy q-inequalities
- 2014
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Ingår i: Czechoslovak Mathematical Journal. - : Institute of Mathematics, Czech Academy of Sciences. - 0011-4642 .- 1572-9141. ; 64:3, s. 659-682
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Tidskriftsartikel (refereegranskat)abstract
- Some $q$-analysis variants of Hardy type inequalities of the form \int_0^b \bigg(x^{\alpha-1} \int_0^x t^{-\alpha} f(t) d_q t \bigg)^{\!p} d_q x \leq C \int_0^b f^p(t) d_q t with sharp constant $C$ are proved and discussed. A similar result with the Riemann-Liouville operator involved is also proved. Finally, it is pointed out that by using these techniques we can also obtain some new discrete Hardy and Copson type inequalities in the classical case.
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