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On the boundedness of the differentiation operator between weighted spaces of holomorphic functions

Anahit Harutyunyan, Wolfgang Lusky (2008)

Studia Mathematica

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 f | f | in Besov spaces

Patrick Oswald (1992)

Commentationes Mathematicae Universitatis Carolinae

For 1 p , precise conditions on the parameters are given under which the particular superposition operator T : f | f | is a bounded map in the Besov space B p , q s ( R 1 ) . The proofs rely on linear spline approximation theory.

On the -characteristic of fractional powers of linear operators

Jürgen Appell, Marilda A. Simões, Petr P. Zabrejko (1994)

Commentationes Mathematicae Universitatis Carolinae

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 closure of spaces of sums of ridge functions and the range of the X -ray transform

Jan Boman (1984)

Annales de l'institut Fourier

For a R n { 0 } and Ω an open bounded subset of R n definie L p ( Ω , a ) as the closed subset of L p ( Ω ) consisting of all functions that are constant almost everywhere on almost all lines parallel to a . For a given set of directions a ν R n { 0 } , ν = 1 , ... , m , we study for which Ω it is true that the vector space ( * ) L p ( Ω , a 1 ) + + L p ( Ω , a m ) is a closed subspace of L p ( Ω ) . This 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 Ω R 2 , the boundary...

On the closure of the Lizorkin space in spaces of Beppo Levi type

Takahide Kurokawa (2002)

Studia Mathematica

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 continuity of Bessel potentials in Orlicz spaces.

N. Aïssaoui (1996)

Collectanea Mathematica

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.

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