A new extension of Komlós' theorem in infinite dimensions. Application: Weak compactness in .
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces [Book]
A new function space and applications
We define a new function space , which contains in particular BMO, BV, and , . We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving norms of integer-valued functions in . We introduce a significant closed subspace, , of , containing in particular VMO and , . The above mentioned estimates imply in particular that integer-valued functions belonging to are necessarily constant. This framework provides a “common roof” to various,...
A new look on Hankel forms over Fock space
A New Proof of the Fundamental Lemma of Interpolation Theory.
A new proof of the Jawerth-Franke embedding.
A new relationship between decomposability and convexity
In the present work we prove that, in the space of Pettis integrable functions, any subset that is decomposable and closed with respect to the topology induced by the so-called Alexiewicz norm (where ) is convex. As a consequence, any such family of Pettis integrable functions is also weakly closed.
A non-doubling Trudinger inequality
We establish a Trudinger inequality for functions that satisfy a suitable Poincarè inequality in a Euclidean space equipped with a Borel measure that need not be doubling.
A non-existence theorem for translation invariant operators on weighted L...-spaces.
A nonlinear boundary problem involving the -bi-Laplacian operator.
A nonlinear operator in potential theory
A Norm Preserving Complex Choquet Theorem.
A Normed Linear Space Containing the Schlicht Functions.
A note on a critical problem with natural growth in the gradient
The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes in , on , . This problem is a particular case of problem (2). Notice that is optimal as coefficient and exponent on the right hand side.
A note on a two-weighted Sobolev inequality
A note on Banach algebras that are not isomorphic to a group algebra.
A note on bornivorous barrels of C(X,E).
A Note on compactness in Banach spaces.
A note on compactness-type properties with respect to Lorentz norms of bounded subsets of a Sobolev Space
A note on composition operators on spaces of real analytic functions
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.