Linear operators on and Lorentz spaces: The Krasnosel’skii-Zabrieko characteristic sets
Linear operators on non-locally convex Orlicz spaces
We study linear operators from a non-locally convex Orlicz space to a Banach space . Recall that a linear operator is said to be σ-smooth whenever in implies . It is shown that every σ-smooth operator factors through the inclusion map , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex...
Linear topological classifications of certain function spaces. II.
Linear topological invariants of spaces of holomorphic functions in infinite dimension.
It is shown that if E is a Frechet space with the strong dual E* then Hb(E*), the space of holomorphic functions on E* which are bounded on every bounded set in E*, has the property (DN) when E ∈ (DN) and that Hb(E*) ∈ (Ω) when E ∈ (Ω) and either E* has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V) consisting of holomorphic functions on E* which are equal to 0 on V in H(E*) for every nuclear Frechet space E with E ∈ (DN) ∩ (Ω) is stablished...
Linear topological properties of the Lumer-Smirnov class of the polydisc
Linear topological properties of the Lumer-Smirnov class of the unit polydisc are studied. The topological dual and the Fréchet envelope are described. It is proved that has a weak basis but it is nonseparable in its original topology. Moreover, it is shown that the Orlicz-Pettis theorem fails for .
Linear transformations from a function space
Linearization and compactness
This paper is devoted to several questions concerning linearizations of function spaces. We first consider the relation between linearizations of a given space when it is viewed as a function space over different domains. Then we study the problem of characterizing when a Banach function space admits a Banach linearization in a natural way. Finally, we consider the relevance of compactness properties in linearizations, more precisely, the relation between different compactness properties of a mapping,...
Lions-Peetre reiteration formulas for triples and their applications
We present, discuss and apply two reiteration theorems for triples of quasi-Banach function lattices. Some interpolation results for block-Lorentz spaces and triples of weighted -spaces are proved. By using these results and a wavelet theory approach we calculate (θ,q)-spaces for triples of smooth function spaces (such as Besov spaces, Sobolev spaces, etc.). In contrast to the case of couples, for which even the scale of Besov spaces is not stable under interpolation, for triples we obtain stability...
Lipschitz and bi-Lipschitz functions.
Lipschitz classes and Poisson integrals on stratified groups
Lipschitz continuity in Muckenhoupt 𝓐₁ weighted function spaces
We study continuity envelopes of function spaces and where the weight belongs to the Muckenhoupt class ₁. This essentially extends partial forerunners in [13, 14]. We also indicate some applications of these results.
Lipschitz estimates for multilinear commutator of pseudo-differential operators.
Lipschitz measures and vector-valued Hardy spaces.
Lipschitz spaces and M-ideals.
Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.
Littlewood-Paley theory and ϵ-families of operators
Local inequalities for plurisubharmonic functions.
Local invertibility of non-archimedean vector-valued functions
Local Mappings on spaces of differentiable functions.
Local means and wavelets in function spaces
The paper deals with local means and wavelet bases in weighted and unweighted function spaces of type and on ℝⁿ and on ⁿ.