On the Brudnyi-Krugljak duality theory of spaces formed by the K-method of interpolation.
On the -characteristic of fractional powers of linear operators
We describe the geometric structure of the -characteristic of fractional powers of bounded or compact linear operators over domains with arbitrary measure. The description builds essentially on the Riesz-Thorin and Marcinkiewicz-Stein-Weiss- Ovchinnikov interpolation theorems, as well as on the Krasnosel’skij-Krejn factorization theorem.
On the class of entire Dirichlet functions of several complex variables having finite order point
On the Classification of Complex Lindenstrauss Spaces.
On the closure of modules of continuously differentiable mappings
On the closure of spaces of sums of ridge functions and the range of the -ray transform
For and an open bounded subset of definie as the closed subset of consisting of all functions that are constant almost everywhere on almost all lines parallel to . For a given set of directions , , we study for which it is true that the vector spaceThis problem arizes naturally in the study of image reconstruction from projections (tomography). An essentially equivalent problem is to decide whether a certain matrix-valued differential operator has closed range. If , the boundary...
On the closure of the Lizorkin space in spaces of Beppo Levi type
The purpose of this paper is to give a characterization of the closure of the Lizorkin space in spaces of Beppo Levi type. As preparations for the proof, we establish the invariance of the Lizorkin space, and give local integral representations for smooth functions.
On the coefficient multipliers theorem of Hardy and Littlewood.
On the completeness of -spaces over a charge
On the complex of Sobolev spaces associated with an abstract Hilbert complex.
On the conjugates of some function spaces
On the constants for some Sobolev imbeddings.
On the continuity of Bessel potentials in Orlicz spaces.
It is shown that Bessel capacities in reflexive Orlicz spaces are non increasing under orthogonal projection of sets. This is used to get a continuity of potentials on some subspaces. The obtained results generalize those of Meyers and Reshetnyak in the case of Lebesgue classes.
On the continuity of strongly nonlinear potential
On the Convexity Coefficient of Orlicz Spaces.
On the density of continuous functions in variable exponent Sobolev space.
On the density of smooth functions in certain subspaces of Sobolev space
On the density of smooth functions in Sobolev-Orlicz spaces.
On the dependence of the orthogonal projector on deformations of the scalar product
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
On the diametral dimension of weighted spaces of analytic germs
We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces and for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.