algebras and the symbolic calculus of Sebastião e Silva. (Les algèbres et le calcul symbolique de Sebastião e Silva.)
(,) mapping properties of convolution transforms
-Spaces and injective locally convex spaces [Book]
-absolutely summing operators on the space and applications.
2-microlocal Besov and Triebel-Lizorkin spaces of variable integrability.
A Best Covering Problem.
A bilinear version of Holsztyński's theorem on isometries of C(X)-spaces
We prove that, for a compact metric space X not reduced to a point, the existence of a bilinear mapping ⋄: C(X) × C(X) → C(X) satisfying ||f⋄g|| = ||f|| ||g|| for all f,g ∈ C(X) is equivalent to the uncountability of X. This is derived from a bilinear version of Holsztyński's theorem [3] on isometries of C(X)-spaces, which is also proved in the paper.
A bipolar theorem for L
A capacity approach to the Poincaré inequality and Sobolev imbeddings in variable exponent Sobolev spaces.
We study the Poincaré inequality in Sobolev spaces with variable exponent. Under a rather mild and sharp condition on the exponent p we show that the inequality holds. This condition is satisfied e.g. if the exponent p is continuous in the closure of a convex domain. We also give an essentially sharp condition for the exponent p as to when there exists an imbedding from the Sobolev space to the space of bounded functions.
A Carlson type inequality with blocks and interpolation
An inequality, which generalizes and unifies some recently proved Carlson type inequalities, is proved. The inequality contains a certain number of “blocks” and it is shown that these blocks are, in a sense, optimal and cannot be removed or essentially changed. The proof is based on a special equivalent representation of a concave function (see [6, pp. 320-325]). Our Carlson type inequality is used to characterize Peetre’s interpolation functor (see [26]) and its Gagliardo closure on couples of...
A characterization of C1-convex sets in Sobolev spaces.
A characterization of maps in which can be approximated by smooth maps
A characterization of Orlicz spaces isometric to Lp-spaces.
In this note we present an affirmative answer to the problem posed by M. Baronti and C. Franchetti (oral communication) concerning a characterization of Lp-spaces among Orlicz sequence spaces. In fact, we show a more general characterization of Orlicz spaces isometric to Lp-spaces.
A characterization of regular averaging operators and its consequences
We present a characterization of continuous surjections, between compact metric spaces, admitting a regular averaging operator. Among its consequences, concrete continuous surjections from the Cantor set 𝓒 to [0,1] admitting regular averaging operators are exhibited. Moreover we show that the set of this type of continuous surjections from 𝓒 to [0,1] is dense in the supremum norm in the set of all continuous surjections. The non-metrizable case is also investigated. As a consequence, we obtain...
A characterization of Sobolev spaces via local derivatives
Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function possesses an derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space . Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.
A characterization of some weak semi-continuity of integral functionals
A characterization of subspaces of
A characterization of the duals of some echelon Köthe spaces of Banach valued functions.
A characterization of Valdivia compact spaces.
A characterization of weighted -spaces of holomorphic functions having the dual density condition
We characterize when weighted -spaces of holomorphic functions have the dual density condition, when the weights are radial and grow logarithmically.