DANIEL CARANDO; Sevilla Peris, Pablo(Springer Verlag (Germany), 2014-03)
[EN] We study Hahn-Banach extensions of multilinear forms defined on Banach sequence spaces. We characterize c(0) in terms of extension of bilinear forms, and describe the Banach sequence spaces in which every bilinear ...
[EN] Inspired by a recent article on Frechet spaces of ordinary Dirichlet series Sigma a(n)n(-s) due to J. Bonet, we study topological and geometrical properties of certain scales of Frechet spaces of general Dirichlet ...
[EN] We study the Hardy space of translated Dirichlet series H+. It consists on those Dirichlet series Sigma a(n)n(-s) such that for some (equivalently, every) 1 <= p < infinity, the translation Sigma a(n)n(-(s+ 1/sigma)) ...
[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 ...
Conejero, J. Alberto; Seoane-Sepulveda, Juan B.; Sevilla Peris, Pablo(John Wiley & Sons, 2017)
[EN] We employ a classical result by Toeplitz (1913) and the seminal work by Bohnenblust and Hille on Dirichlet series (1931) to show that the set of continuous m-homogeneous non-analytic polynomials on c(o) contains an ...
[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 study some dynamical properties of composition operators defined on the space P(^m X) of m-homogeneous polynomials on a Banach space X when P(^m X) is endowed with two different topologies: the one of uniform ...
[EN] We study mean ergodic composition operators on infinite dimensional spaces of holomorphic functions of different types when defined on the unit ball of a Banach or a Hilbert space: that of all holomorphic functions, ...
[EN] We develop a novel decomposition of the monomials in order to study the set of monomial convergence for spaces of holomorphic functions over l(r) for 1 < r <= 2. For H-b. (l(r)), the space of entire functions of bounded ...
Carando, Daniel; Dimant, Veronica; Sevilla Peris, Pablo(Institute of Mathematics, Polish Academy of Sciences, 2009)
[EN] We establish Holder-type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain ...
[EN] Let H-infinity be the set of all ordinary Dirichlet series D = Sigma(n) a(n)(n-1) ann-s representing bounded holomorphic functions on the right half plane. A completely multiplicative sequence (b(n)) of complex numbers ...
[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 ...
Dimant, Verónica; Sevilla Peris, Pablo(Universitat Autonoma de Barcelona, 2016)
[EN] We investigate the summability of the coefficients of m-homogeneous polynomials and m-linear mappings defined on l(p) spaces. In our research we obtain results on the summability of the coefficients of m-linear mappings ...
Defant, Andreas; Sevilla Peris, Pablo(Adam Mickiewicz University The Faculty of Mathematics and Computer Science, 2014)
[EN] In 1931 H.F.Bohnenblust and E.Hille published a very important paper in which
not only did they solve a long standing problem on convergence of Dirichlet series, but also
gave a general version of a celebrated ...
We give a variant of the Bohenblust-Hille inequality which, for certain families of polynomials, leads to constants with polynomial growth in the degree.
Defant, Andreas; Sevilla Peris, Pablo(Institute of Mathematics, Polish Academy of Sciences, 2016)
[EN] Let x(m, n) be the unconditional basis constant of the monomial basis Z alpha, alpha is an element of N(0)n with vertical bar alpha vertical bar = m, of the Banach space of all m-homogeneous polynomials inn complex ...