On Strongly WCG Banach Spaces.
On subnormal operators whose spectrum are multiply connected domains.
On subspaces of H¹ isomorphic to H¹
On subspaces of Orlicz sequences spaces
On Taylor functional calculus
On tensor products of continuous functions
On the -Laplacian.
On the algebraic properties of the spaces
We investigate the multiplicative properties of the spaces As in the case of the classical Sobolev spaces this space does not form an algebra. We investigate instead the space , more precisely a subspace of it formed by products of solutions of the homogeneous wave equation with data in .
On the approximation of continuosly diffentialble functions in Hilbert spaces
On the approximation of the exterior Stokes problem in three dimensions
On the Banach algebra .
On the Banach envelopes of Hardy-Orlicz spaces on an annulus
We describe the Banach envelopes of Hardy-Orlicz spaces of analytic functions on an annulus in the complex plane generated by Orlicz functions well-estimated by power-type functions.
On the Banach-Mazur distance between continuous function spaces with scattered boundaries
We study the dependence of the Banach-Mazur distance between two subspaces of vector-valued continuous functions on the scattered structure of their boundaries. In the spirit of a result of Y. Gordon (1970), we show that the constant appearing in the Amir-Cambern theorem may be replaced by for some class of subspaces. We achieve this by showing that the Banach-Mazur distance of two function spaces is at least 3, if the height of the set of weak peak points of one of the spaces differs from the...
On the Banach-Stone problem
Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of then T can be written as a weighted composition...
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.