On the Banach-Stone Theorem.
On the Beurling-Lax theorem for domains with one hole.
On the Bloch space and convolution of functions in the Lp-valued case.
On the boundedness of classical operators on weighted Lorentz spaces.
On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
On the boundedness of the mapping in Besov spaces
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
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