| 1. |
- Johansson, Maria, et al.
(författare)
-
Hardy inequality with three measures on monotone functions
- 2008
-
Ingår i: Mathematical Inequalities & Applications. - : Element d.o.o.. - 1331-4343 .- 1848-9966. ; 11:3, s. 393-413
-
Tidskriftsartikel (refereegranskat)abstract
- Characterization of Lvp[0, ∞) - L μq[O, ∞) boundedness of the general Hardy operator (Hsf)(x) =(∫[0,x] fsudλ) 1/s restricted to monotone functions f ≥ 0 for 0 < p.q.s < ∞ with positive Borel σ -finite measures λ, μ and v is obtained.
|
|
| 2. |
- Persson, Lars-Erik, et al.
(författare)
-
Some scales of equivalent weight characterizations of Hardy´s inequality: the case q < p
- 2007
-
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.
|
|
| 3. |
- Persson, Lars-Erik, et al.
(författare)
-
Weighted Hardy-type inequalities on the cone of quasi-concave functions
- 2014
-
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.
|
|
| 4. |
- Stepanov, Vladimir D., et al.
(författare)
-
ALTERNATIVE CRITERIA FOR THE BOUNDEDNESS OF VOLTERRA INTEGRAL OPERATORS IN LEBESGUE SPACES
- 2009
-
Ingår i: Mathematical Inequalities & Applications. - 1331-4343 .- 1848-9966. ; 12:4, s. 873-889
-
Tidskriftsartikel (refereegranskat)abstract
- Three different criteria for L-p - L-q boundedness of Volterra integral operator (1.1) with locally integrable weight functions w, v and a non-negative kernel k(x, y) satisfying Oinarov's condition for each case 1 < p <= q < infinity and 1 < q < p < infinity are given. Relations between components of the boundedness constants are described.
|
|
| 5. |
- Stepanov, Vladimir D., et al.
(författare)
-
Kernel operators with variable intervals of integration in Lebesgue spaces and applications
- 2010
-
Ingår i: Mathematical Inequalities & Applications. - 1331-4343 .- 1848-9966. ; 13:3, s. 449-510
-
Tidskriftsartikel (refereegranskat)abstract
- New criteria of L-p - L-q boundedness of Hardy-Steklov type operator (1.1) with both increasing on (0, infinity) boundary functions a(x) and b(x) are obtained for 1 < p <= q < infinity and 0 < q < p < infinity, p > 1. This result is applied for two-weighted L-p - L-q characterization of the corresponding geometric Steklov operator (1.3) and other related problems.
|
|
