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- Approximation in Morrey spacesPublication . Almeida, Alexandre; Samko, StefanA new subspace of Morrey spaces whose elements can be approximated by infinitely differentiable compactly supported functions is introduced. Consequently, we give an explicit description of the closure of the set of such functions in Morrey spaces. A generalisation of known embeddings of Morrey spaces into weighted Lebesgue spaces is also obtained. (C) 2016 Elsevier Inc. All rights reserved.
- Maximal operator with rough kernel in variable musielak-morrey-orlicz type spaces, variable herz spaces and grand variable lebesgue spacesPublication . Rafeiro, Humberto; Samko, StefanIn the frameworks of some non-standard function spaces (viz. Musielak-Orlicz spaces, generalized Orlicz-Morrey spaces, generalized variable Morrey spaces and variable Herz spaces) we prove the boundedness of the maximal operator with rough kernel. The results are new even for p constant.
- Morrey spaces are closely embedded between vanishing stummel spacesPublication . Samko, StefanWe prove a new property of Morrey function spaces by showing that the generalized local Morrey spaces are embedded between weighted Lebesgue spaces with weights differing only by a logarithmic factor. This leads to the statement that the generalized global Morrey spaces are embedded between two generalized Stummel classes whose characteristics similarly differ by a logarithmic factor. We give examples proving that these embeddings are strict. For the generalized Stummel spaces we also give an equivalent norm.
- Riesz fractional integrals in grand lebesgue spaces on ℝnPublication . Samko, Stefan; Umarkhadzhiev, SalaudinWe introduce conditions on the construction of grand Lebesgue spaces on R-n which imply the validity of the Sobolev theorem for the Riesz fractional integrals I-alpha and the boundedness of the maximal operator, in such spaces. We also give an inversion of the operator I-alpha by means of hypersingular integrals, within the frameworks of the introduced spaces. We also proof the denseness of C-0(infinity)(R-n) in a subspace of the considered grand space.
- Some sharp inequalities for multidimensional integral operators with homogeneous kernel: an overview and new resultsPublication . Lukkassen, D.; Persson, L. E.; Samko, Stefan; Wall, P.One goal of this paper is to point out the fact that a big number of inequalities proved from time to time in journal publications, both one-dimensional and multi-dimensional, are particular cases of some general results for integral operators with homogeneous kernels, including in particular, the statements on sharp constants.Some new multidimensional Hardy-Hilbert type inequalities are derived. Moreover, a new multidimensional Polya-Knopp inequality is proved and some examples of applications are derived from this result. The constants in all inequalities are sharp.
- Corrigendum to "hardy type inequality in variable lebesgue spaces"Publication . Rafeiro, Humberto; Samko, StefanIn this note, we correct a gap made in the assumptions of the final results of the paper [1]. We give these results with corrected formulations and provide a proof of some auxiliary result which allows us to simultaneously admit regions more general than used in [1].
- On maximal and potential operators with rough kernels in variable exponent spacesPublication . Rafeiro, Humberto; Samko, StefanIn the framework of variable exponent Lebesgue and Morrey spaces we prove some boundedness results for operators with rough kernels, such as the maximal operator, fractional maximal operator, sharp maximal operators and fractional operators. The approach is based on some pointwise estimates.
- Maximal, potential and singular operators in the local "complementary" variable exponent Morrey type spacesPublication . Guliyev, Vagif S.; Hasanov, Javanshir J.; Samko, StefanWe consider local "complementary" generalized Morrey spaces M-c({x0})p(.).omega (Omega) in which the p-means of function are controlled over Omega \ B(x(0), r) instead of B(x(0), r), where Omega subset of R-n is a bounded open set, p(x) is a variable exponent, and no monotonicity type condition is imposed onto the function omega(r) defining the "complementary" Morrey-type norm. In the case where omega is a power function, we reveal the relation of these spaces to weighted Lebesgue spaces. In the general case we prove the boundedness of the Hardy-Littlewood maximal operator and Calderon-Zygmund singular operators with standard kernel, in such spaces. We also prove a Sobolev type M-c({x0})p(.).omega (Omega) -> M-c({x0})p(.).omega (Omega)-theorem for the potential operators I-alpha(.), also of variable order. In all the cases the conditions for the boundedness are given it terms of Zygmund-type integral inequalities-on omega(r), which do not assume any assumption on monotonicity of omega(r).
- Mixed norm Bergman-Morrey-type spaces on the unit discPublication . Samko, Stefan; Karapetyants, A. N.We introduce and study the mixed-norm Bergman-Morrey space A (q;p,lambda) , mixednorm Bergman-Morrey space of local type A (loc) (q;p,lambda) , and mixed-norm Bergman-Morrey space of complementary type (C) A (q;p,lambda) on the unit disk D in the complex plane C. Themixed norm Lebesgue-Morrey space L (q;p,lambda) is defined by the requirement that the sequence of Morrey L (p,lambda)(I)-norms of the Fourier coefficients of a function f belongs to l (q) (I = (0, 1)). Then, A (q;p,lambda) is defined as the subspace of analytic functions in L (q;p,lambda) . Two other spaces A q;p,lambda loc and (C) A (q;p,lambda) are defined similarly by using the local Morrey L (loc) (p,lambda) (I)-norm and the complementary Morrey (C) L (p,lambda)(I)-norm respectively. The introduced spaces inherit features of both Bergman and Morrey spaces and, therefore, we call them Bergman-Morrey-type spaces. We prove the boundedness of the Bergman projection and reveal some facts on equivalent description of these spaces.
- A note on Riesz fractional integrals in the limiting case alpha(x)p(x) a parts per thousand nPublication . Samko, StefanWe show that the Riesz fractional integration operator I (alpha(center dot)) of variable order on a bounded open set in Omega aS, a"e (n) in the limiting Sobolev case is bounded from L (p(center dot))(Omega) into BMO(Omega), if p(x) satisfies the standard logcondition and alpha(x) is Holder continuous of an arbitrarily small order.
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