A free boundary problem involving limiting Sobolev exponents.
A full characterization of multipliers for the strong -integral in the euclidean space
We study a generalization of the classical Henstock-Kurzweil integral, known as the strong -integral, introduced by Jarník and Kurzweil. Let be the space of all strongly -integrable functions on a multidimensional compact interval , equipped with the Alexiewicz norm . We show that each element in the dual space of can be represented as a strong -integral. Consequently, we prove that is strongly -integrable on for each strongly -integrable function if and only if is almost everywhere...
A function parameter in connection with interpolation of Banach spaces.
A function space C(K) not weakly homeomorphic to C(K)×C(K)
A function space Cp(X) not linearly homeomorphic to Cp(X) × ℝ
We construct two examples of infinite spaces X such that there is no continuous linear surjection from the space of continuous functions onto × ℝcp(X)cp(X). One of these examples is compact. This answers some questions of Arkhangel’skiĭ.
A Gagliardo-Nirenberg inequality, with application to duality-based a posteriori estimation in the L^1 norm
A General Approach to Infinite-Dimensional Holomorphy.
A general approximation theorem of Whitney type.
We show that Whitney?s approximation theorem holds in a general setting including spaces of (ultra)differentiable functions and ultradistributions. This is used to obtain real analytic modifications for differentiable functions including optimal estimates. Finally, a surjectivity criterion for continuous linear operators between Fréchet sheaves is deduced, which can be applied to the boundary value problem for holomorphic functions and to convolution operators in spaces of ultradifferentiable functions...
A general description of the Bergman projection
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 a theorem of H. Brezis & F. E. Browder and applications to some unilateral problems
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 Signorini's perturbation method suggested by two problems of Grioli
A generalization of the Banach-Stone theorem
A generalization of the Lions-Temam compact imbedding theorem
A generalization of the Shimogaki theorem
A Generalization of the Strict Topology.