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.
A generalized projection decomposition in Orlicz-Bochner spaces
In this paper, a precise projection decomposition in reflexive, smooth and strictly convex Orlicz-Bochner spaces is given by the representation of the duality mapping. As an application, a representation of the metric projection operator on a closed hyperplane is presented.
A geometrical/combinatorical question with implications for the John-Nirenberg inequality for BMO functions
The first and last sections of this paper are intended for a general mathematical audience. In addition to some very brief remarks of a somewhat historical nature, we pose a rather simply formulated question in the realm of (discrete) geometry. This question has arisen in connection with a recently developed approach for studying various versions of the function space BMO. We describe that approach and the results that it gives. Special cases of one of our results give alternative proofs of the...
A kind of estimate of difference norms in anisotropic weighted Sobolev-Lorentz spaces.