| 41. |
- Pecaric, Josip, et al.
(författare)
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On sharpness of some integral inequalities and an integral equation of Volterra type
- 2002
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 5:4, s. 659-670
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Tidskriftsartikel (refereegranskat)abstract
- The sharpness of some recent integral inequalities is discussed and the corresponding external functions are pointed out. It is also proved that the cases of equality can equivalently be obtained by solving an integral equation of Volterra type with discontinous kemel χA (t). This integral equation of independent interest is solved for every measurable set A on (a, b), -∞ < a < b < ∞.
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| 42. |
- Peric, Ivan, et al.
(författare)
-
Sharp integral inequalities for C-monotone functions of several variables
- 2000
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 3:1, s. 51-62
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Tidskriftsartikel (refereegranskat)abstract
- Some sharp integral inequalities for C-monotone functions of several variables are proved. All cases of equality are found and some related results are pointed out and discussed.
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| 43. |
- Persson, Lars-Erik, et al.
(författare)
-
Quasi-monotone weight functions and their characteristics and applications
- 2012
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 15:3, s. 685-705
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Tidskriftsartikel (refereegranskat)abstract
- A weight function w(x) on (0,l) or (l,infinity), is said to be quasi-monotone if w(x)x(-a0) <= C(0)w(y)y(-a0) either for all x <= y or for all y <= x, for some a(0) is an element of R, C-0 >= 1. In this paper we discuss, complement and unify several results concerning quasi-monotone functions. In particular, some new results concerning the close connection to index numbers and generalized Bary-Stechkin classes are proved and applied. Moreover, some new regularization results are proved and several applications are pointed out, e. g. in interpolation theory, Fourier analysis, Hardy-type inequalities, singular operators and homogenization theory.
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| 44. |
- Persson, Lars-Erik, et al.
(författare)
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Some difference inequalities with weights and interpolation
- 1998
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 1:3, s. 437-444
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Tidskriftsartikel (refereegranskat)abstract
- The well-known Grisvard-Jakovlev inequality (see Theorems 1 and 1_ ) can be interpretedas a fractional order Hardy inequality or as a weighted difference inequality. Someinequalities of this type have been recently proved and discussed by the authors and H. Heinig,and this paper coincides mostly with a lecture held by the first author at the International workshopon difference and differential inequalities (July 3 - 7, 1996, Marmara Research Center,Turkey) where some historical remarks, ideas and results from the papers of the authors and H.Heinig have been presented. Additionally we present and prove some new difference inequalitieswith weights. Mostly, we omit the proofs which can be found in the papers mentioned and in thereferences there, and for simplicity, we consider functions on the interval
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| 45. |
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| 46. |
- Persson, Lars-Erik, et al.
(författare)
-
Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:2, s. 267-279
-
Tidskriftsartikel (refereegranskat)abstract
- We consider the weighted Hardy inequality 1/q 1/p q ∞ ∞ x f p (x)v(x)dx f (t)dt u(x)dx C 0 0 0for the case 0 < q < p < ∞, p > 1 . The weights u(x) and v(x) for which this inequalityholds for all f (x) 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanovconditions. In this paper, we show that these conditions are not unique and can be supplementedby some continuous scales of conditions and we prove their equivalence. The results for the dualoperator which do not follow by duality when 0 < q < 1 are also given.
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| 47. |
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| 48. |
- Persson, Lars-Erik, et al.
(författare)
-
Weighted Hardy-type inequalities on the cone of quasi-concave functions
- 2014
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 17:3, s. 879-898
-
Tidskriftsartikel (refereegranskat)abstract
- The paper is devoted to the study of weighted Hardy-type inequalities on the cone of quasi-concave functions, which is equivalent to the study of the boundedness of the Hardy operator between the Lorentz Γ-spaces. For described inequalities we obtain necessary and sufficient conditions to hold for parameters q 1, p > 0 and sufficient conditions for the rest of the range of parameters.
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| 49. |
- Persson, Lars-Erik, et al.
(författare)
-
Weighted inequalities of Hardy type for matrix operators: The case q
- 2007
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Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 10:4, s. 843-861
-
Tidskriftsartikel (refereegranskat)abstract
- A non-negative triangular matrix operator is considered in weighted Lebesgue spaces ofsequences. Under some additional conditions on the matrix, some new weight characterizationsfor discrete Hardy type inequalities with matrix operator are proved for the case 1 < q < p < ∞.Some further results are pointed out.
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| 50. |
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