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Complex Convexity of Orlicz-Lorentz Spaces and its Applications

Changsun Choi, Anna Kamińska, Han Ju Lee (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

We give sufficient and necessary conditions for complex extreme points of the unit ball of Orlicz-Lorentz spaces, as well as we find criteria for the complex rotundity and uniform complex rotundity of these spaces. As an application we show that the set of norm-attaining operators is dense in the space of bounded linear operators from d * ( w , 1 ) into d(w,1), where d * ( w , 1 ) is a predual of a complex Lorentz sequence space d(w,1), if and only if wi ∈ c₀∖ℓ₂.

Complex interpolation of function spaces with general weights

Douadi Drihem (2023)

Commentationes Mathematicae Universitatis Carolinae

We present the complex interpolation of Besov and Triebel–Lizorkin spaces with generalized smoothness. In some particular cases these function spaces are just weighted Besov and Triebel–Lizorkin spaces. As a corollary of our results, we obtain the complex interpolation between the weighted Triebel–Lizorkin spaces F ˙ p 0 , q 0 s 0 ( ω 0 ) and F ˙ ∞ , q 1 s 1 ( ω 1 ) with suitable assumptions on the parameters s 0 , s 1 , p 0 , q 0 and q 1 , and the pair of weights ( ω 0 , ω 1 ) .

Composition in ultradifferentiable classes

Armin Rainer, Gerhard Schindl (2014)

Studia Mathematica

We characterize stability under composition of ultradifferentiable classes defined by weight sequences M, by weight functions ω, and, more generally, by weight matrices , and investigate continuity of composition (g,f) ↦ f ∘ g. In addition, we represent the Beurling space ( ω ) and the Roumieu space ω as intersection and union of spaces ( M ) and M for associated weight sequences, respectively.

Composition operator and Sobolev-Lorentz spaces W L n , q

Stanislav Hencl, Luděk Kleprlík, Jan Malý (2014)

Studia Mathematica

Let Ω,Ω’ ⊂ ℝⁿ be domains and let f: Ω → Ω’ be a homeomorphism. We show that if the composition operator T f : u ↦ u ∘ f maps the Sobolev-Lorentz space W L n , q ( Ω ' ) to W L n , q ( Ω ) for some q ≠ n then f must be a locally bilipschitz mapping.

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