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...
A difference between continuous and absolutely continuous norms in Banach function spaces
On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.
A difference quotient norm for spaces of quasi-homogeneous Bessel potentials
A disjointness property of sequences in
A factorization theorem in Banach lattices and its application to Lorentz spaces
-convexity and -concavity of a Banach lattice are characterized by factorization of multiplication operators from into through . This characterization is applied to calculate the concavity type of Lorentz spaces.
A few remarks on the results of Rosinski and Suchanecki concerning unconditional convergence and -sequences
A formula for the functions realizing functionals.
A function parameter in connection with interpolation of Banach spaces.
A general differentiation theorem for multiparameter additive processes
Let be a Banach lattice of equivalence classes of real-valued measurable functions on a σ-finite measure space and be a strongly continuous locally bounded d-dimensional semigroup of positive linear operators on L. Under suitable conditions on the Banach lattice L we prove a general differentiation theorem for locally bounded d-dimensional processes in L which are additive with respect to the semigroup T.
A general differentiation theorem for superadditive processes
Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=: t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.
A general result on the equivalence between derivation of integrals and weak inequalities for the Hardy-Littlewood maximal operator
A generalization of Dirichlet's unit theorem
We generalize Dirichlet's S-unit theorem from the usual group of S-units of a number field K to the infinite rank group of all algebraic numbers having nontrivial valuations only on places lying over S. Specifically, we demonstrate that the group of algebraic S-units modulo torsion is a ℚ-vector space which, when normed by the Weil height, spans a hyperplane determined by the product formula, and that the elements of this vector space which are linearly independent over ℚ retain their linear independence...
A generalization of Riesz-Fischer theorem
A generalization of the Lions-Temam compact imbedding theorem
A generalization of the Shimogaki theorem
A generalized dual maximizer for the Monge–Kantorovich transport problem
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
A generalized dual maximizer for the Monge–Kantorovich transport problem∗
The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y → [0,∞] is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic...
A generalized mixed topology on Orlicz spaces.