| 1. |
- Barza, Sorina, et al.
(författare)
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On weighted multidimensional embeddings for monotone functions
- 2001
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Ingår i: Mathematica Scandinavica. - : Det Kgl. Bibliotek/Royal Danish Library. - 0025-5521 .- 1903-1807. ; 88:2, s. 303-319
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Tidskriftsartikel (refereegranskat)abstract
- We characterize the inequality (∫RN+ fqu)1/q ≤ C(∫RN+fpv)1/p, 0 < q, p < ∞, for monotone functions f ≥ 0 and nonnegative weights u and v. The case q < p is new and the case 0 < p ≤ q < ∞ is extended to a modular inequality with N-functions. A remarkable fact concerning the calculation of C is pointed out
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| 2. |
- Gogatishvili, Amiran, et al.
(författare)
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Some scales of equivalent conditions to characterize the Stieltjes inequality : the case q
- 2014
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Ingår i: Mathematische Nachrichten. - : Wiley. - 0025-584X .- 1522-2616. ; 287:2-3, s. 242-253
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the weighted Stieltjes inequality can be characterized by four different scales of conditions also for the case , . In particular, a new proof of a result of G. Sinnamon is given, which also covers the case . Moreover, for the situation at hand a new gluing theorem and also an equivalence theorem of independent interest are proved and discussed. By applying our new equivalence theorem to weighted inequalities for the Stieltjes transform we obtain the four new scales of conditions for characterization of Stieltjes inequality
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| 3. |
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| 4. |
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| 5. |
- Persson, Lars-Erik, et al.
(författare)
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Hardy-type inequalities on the weighted cones of quasi-concave functions
- 2015
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Ingår i: Banach Journal of Mathematical Analysis. - : Springer Science and Business Media LLC. - 1735-8787. ; 9:2, s. 21-34
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Tidskriftsartikel (refereegranskat)abstract
- The complete characterization of the Hardy-type Lp-Lq inequalities on the weighted cones of quasi-concave functions for all 0 < p, q < ∞ is given.
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| 6. |
- Persson, Lars-Erik, et al.
(författare)
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On integral operators with monotone kernels
- 2005
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Ingår i: Doklady Akademii Nauk. - 0869-5652. ; 403:1, s. 11-14
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Tidskriftsartikel (refereegranskat)abstract
- The conditions are investigated, under which for all Lebesgue measurable functions f(x) greater than or equal 0 on a semi-axis R+:=(0, infinity ) with a constant C greater than or equal 0 independent of f, satisfied is inequality: {0 integral infinity [Kf(x)]qν(x)dx}1/q [less-than or equal to] C{0 integral infinity [f(x)]pu(x)dx}1/p (1) with measurable weighted functions u(x) greater than or equal 0 and ν(x) greater than or equal 0 and integral operator Kf(x):=0 integral infinity k(x,y)f(y)dy, where measurable in R+×R+ kernel k(x,y) greater than or equal 0 is monotone in one or two variables. Such operators can be exemplified with Laplace, Hilbert transforms etc. Further, the comparison theorems for (1)-type inequalities with the similar inequalities on a cone of non-growing functions for certain-type Volterra operators are proved.
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| 7. |
- Persson, Lars-Erik, et al.
(författare)
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Two-sided hardy-type inequalities for monotone functions
- 2010
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Ingår i: Complex Variables and Elliptic Equations. - : Informa UK Limited. - 1747-6933 .- 1747-6941. ; 55:8, s. 973-989
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Tidskriftsartikel (refereegranskat)abstract
- We consider Hardy-type operators on the cones of monotone functions with general positive σ-finite Borel measure. Some two-sided Hardy-type inequalities are proved for the parameter -∞ < p < ∞. It is pointed out that such equivalences, in particular, imply a new characterization of the discrete Hardy inequality for the (most difficult) case 0 < q < p ≤ 1
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| 8. |
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| 9. |
- Persson, Lars-Erik, et al.
(författare)
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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
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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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| 10. |
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