Browsing by Author "Persson, Lars-Erik"
Now showing 1 - 4 of 4
Results Per Page
Sort Options
- Some sharp inequalities for integral operators with homogeneous kernelPublication . Lukkassen, Dag; Persson, Lars-Erik; Samko, StefanOne goal of this paper is to show that a big number of inequalities for functions in L-p(R+), 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 < p < 1. Some useful new variants of these results are pointed out and a number of known and new Hardy-Hilbert type inequalities are derived. Moreover, a new Polya-Knopp (geometric mean) inequality is derived and applied. The constants in all inequalities in this paper are sharp.
- Weighted Hardy and potential operators in the generalized Morrey spacesPublication . Persson, Lars-Erik; Samko, NatashaWe study the weighted p -> q-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces L-p.phi(R-n, w) defined by an almost increasing function phi(r) and radial type weight w(vertical bar x vertical bar). We obtain sufficient conditions, in terms of some integral inequalities imposed on phi and w, for such a p -> q-boundedness. In some cases the obtained conditions are also necessary. These results are applied to derive a similar weighted p -> q-boundedness of the Riesz potential operator. (c) 2010 Elsevier Inc. All rights reserved.
- Weighted hardy operators in complementary morrey spacesPublication . Lukkassen, Dag; Persson, Lars-Erik; Samko, StefanWe 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.
- Weighted hardy-type inequalities in variable exponent morrey-type spacesPublication . Lukkassen, Dag; Persson, Lars-Erik; Samko, Stefan; Wall, PeterWe 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.