A Best Covering Problem.
A bipolar theorem for L
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 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 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 class of Banach lattices and positive operators
A class of Banach sequence spaces analogous to the space of Popov
Hagler and the first named author introduced a class of hereditarily Banach spaces which do not possess the Schur property. Then the first author extended these spaces to a class of hereditarily Banach spaces for . Here we use these spaces to introduce a new class of hereditarily Banach spaces analogous of the space of Popov. In particular, for the spaces are further examples of hereditarily Banach spaces failing the Schur property.
A class of special Hardy-Orlicz spaces and the space of BMOA functions
A class of weighted convolution Fréchet algebras
For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists m ∈ ℕ such that...
A compact imbedding result of Lipschitz manifolds.
A compactness criterion of mixed Krasnoselskiĭ-Riesz type in regular ideal spaces of vector functions.
A comparison between the closed modular ideals in l...(w) and L...(w).
A condition implying boundedness and VMO for a function f
Some boundedness and VMO results are proved for a function f integrable on a cube , starting from an integral bound.
A condition of Busemann-Feller type for the derivation of integrals of functions in the class Φ (L).
A continuous surjection from the unit interval onto the unit square.
A counterexample to the L² estimate //Xyu//...C(//X...u// + //Y...u// + //u//).
A density theorem.
A description of Banach space-valued Orlicz hearts
Let Y be a Banach space, (Ω, Σ; μ) a probability space and φ a finite Young function. It is shown that the Y-valued Orlicz heart H φ(μ, Y) is isometrically isomorphic to the l-completed tensor product of the scalar-valued Orlicz heart Hφ(μ) and Y, in the sense of Chaney and Schaefer. As an application, a characterization is given of the equality of and in terms of the Radon-Nikodým property on Y. Convergence of norm-bounded martingales in H φ(μ, Y) is characterized in terms of the Radon-Nikodým...