We give a self-contained treatment of symmetric Banach sequence spaces and some of their natural properties. We are particularly interested in the symmetry of the norm and the existence of symmetric linear functionals. ...

We study the holomorphic functions on a complex Banach space E that are invariant under the action of a given group of operators on E. A great variety of situations occur depending, of course, on the group and the space. ...

We study 'H POT.1' versus 'C POT.1' local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of O(N). These functionals, in many cases, ...

We show that the Poisson maximal operator for the tube over the light-cone, P*, is bounded in the weighted space L p (w) if and only if the weight w(x) belongs to the Muckenhoupt class A p . We also characterize with a ...

In the study of the spectra of algebras of holomorphic functions on a Banach space E, the bidual E″ has a central role, and the spectrum is often shown to be locally homeomorphic to E″. In this paper we consider the problem ...

For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions ...