[EN] Hartman proved in 1939 that the width of the largest possible strip in the complex plane on which a Dirichlet series is uniformly a.s.- sign convergent (i.e., converges uniformly for almost all sequences of signs ...
[EN] The Bohr–Bohnenblust–Hille theorem states that the width of the strip in the complex plane on which an
ordinary Dirichlet series P
n
ann
−s
converges uniformly but not absolutely is less than or equal to 1
2
, ...
[EN] The Cluster Value Theorem is known for being a weak version of the classical Corona Theorem. Given a Banach space X, we study the Cluster Value Problem for the ball algebra A(u)(B-X), the Banach algebra of all uniformly ...
[EN] While the article was in publication process, we found a mistake in a key tool for the proof one of the main results. As a consequence, our result on the ball A(u)(B-X) algebra remains open. For the algebra H-b(X) we ...
[EN] Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities ...
[EN] We study Hausdorff-Young-type inequalities for vector-valued Dirichlet series which allow us to compare the norm of a Dirichlet series in the Hardy space H-p(X) with the q-norm of its coefficients. In order to obtain ...
[EN] Since the concept of limit order is a useful tool to study operator ideals, we
propose an analogous definition for ideals of multilinear forms. From the limit orders
of some special ideals (of nuclear, integral, ...
[EN] We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st. and cotype, and spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get ...
[EN] We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder ...
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.