| 1. |
- Lukkassen, Dag, et al.
(författare)
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Some sharp inequalities for integral operators with homogeneous kernel
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; 2016
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Tidskriftsartikel (refereegranskat)abstract
- One goal of this paper is to show that a big number of inequalities for functions in L p (R + ) Lp(R+), p≥1 p≥1, proved from time to time in journal publications are particular cases of some known general results for integral operators with homogeneous kernels including, in particular, the statements on sharp constants. Some new results are also included, e.g. the similar general equivalence result is proved and applied for 0
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| 2. |
- Lukkassen, Dag, et al.
(författare)
-
Weighted Hardy operators in complementary Morrey spaces
- 2012
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965.
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Tidskriftsartikel (refereegranskat)abstract
- We study the weighted p -> q-boundedness of the multidimensional weighted Hardy-type operators H-omega(alpha) and H-omega(alpha) with radial type weight omega = omega(vertical bar x vertical bar), in the generalized complementary Morrey spaces (C) L-(0)(p,psi) (R-n) defined by an almost increasing function psi = psi(r). We prove a theorem which provides conditions, in terms of some integral inequalities imposed on psi and omega, for such a boundedness. These conditions are sufficient in the general case, but we prove that they are also necessary when the function psi and the weight omega are power functions. We also prove that the spaces (C) L-(0)(p,psi) (Omega) over bounded domains Omega are embedded between weighted Lebesgue space L-p with the weight psi and such a space with the weight psi, perturbed by a logarithmic factor. Both the embeddings are sharp
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| 3. |
- Lukkassen, Dag, et al.
(författare)
-
Weighted Hardy-type inequalities in variable exponent Morrey-type spaces
- 2013
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Ingår i: Journal of Function Spaces and Applications. - : Hindawi Limited. - 0972-6802 .- 1758-4965.
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Tidskriftsartikel (refereegranskat)abstract
- We study the p(.) -> q(.) boundedness of weighted multidimensional Hardy-type operators H-w(alpha(.)) and H-w(alpha(.)) of variable order alpha(x), with radial weight w(vertical bar x vertical bar), from a variable exponent locally generalized Morrey space L-p(.),L-phi(.)(R-n, w) to another L-q(.),L-psi(.)(R-n, w). The exponents are assumed to satisfy the decay condition at the origin and infinity. We construct certain functions, defined by p, alpha, and phi, the belongness of which to the resulting space L-q(.),L-psi(.)(R-n, w) is sufficient for such a boundedness. Under additional assumptions on phi/w, this condition is also necessary. We also give the boundedness conditions in terms of Zygmund-type integral inequalities for the functions phi and phi/w.
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