| 1. |
- 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. |
- Abylayeva, Akbota M., et al.
(författare)
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Boundedness and compactness of a class of Hardy type operators
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.
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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. |
- 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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| 5. |
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| 6. |
- Oinarov, Ryskul, et al.
(författare)
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OSCILLATORY AND SPECTRAL PROPERTIES OF A CLASS OF FOURTH-ORDER DIFFERENTIAL OPERATORS VIA A NEW HARDY-TYPE INEQUALITY
- 2024
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Ingår i: Mathematical Inequalities & Applications. - : ELEMENT. - 1331-4343 .- 1848-9966. ; 27:1, s. 63-83
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by first proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for functions satisfying certain boundary conditions that depend on the boundary behavior of one of its weights at infinity and at zero.
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| 7. |
- Persson, Lars-Erik, et al.
(författare)
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Hardy-type inequalities in fractional h-discrete calculus
- 2018
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- The first power weighted version of Hardy’s inequality can be rewritten as∫∞0(xα−1∫x01tαf(t)dt)pdx≤[pp−α−1]p∫∞0fp(x)dx,f≥0,p≥1,α
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