We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.
In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.
The paper deals with quarkonial decompositions and entropy numbers in weighted function spaces on hyperbolic manifolds. We use these results to develop a spectral theory of related Schrödinger operators in these hyperbolic worlds.
It is well known that any function algebra has an essential set. In this note we define an essential set for an arbitrary function space (not necessarily algebra) and prove that any function space has an essential set.
Function spaces of type Bspq and Fspq cover as special cases classical and fractional Sobolev spaces, classical Besov spaces, Hölder-Zygmund spaces and inhomogeneous Hardy spaces. In the last 2 or 3 decades they haven been studied preferably on Rn and in smooth bounded domains in Rn including numerous applications to pseudodifferential operators, elliptic boundary value problems etc. To a lesser extent spaces of this type have been considered in Lipschitz domains. But in recent times there is a...
We prove several stability properties for the class of compact Hausdorff spaces such that with the weak or the pointwise topology is in the class of Stegall. In particular, this class is closed under arbitrary products.
Nikolskii spaces were defined by way of translations on and by way of coordinate maps on a differentiable manifold. In this paper we prove that, for functions with compact support in , we get an equivalent definition if we replace translations by all isometries of . This result seems to justify a definition of Nikolskii type function spaces on riemannian manifolds by means of a transitive group of isometries (provided that one exists). By approximation theorems, we prove that - for homogeneous...
We consider two types of Besov spaces on the closed snowflake, defined by traces and with the help of the homeomorphic map from the interval [0,3]. We compare these spaces and characterize them in terms of Daubechies wavelets.
It is shown that there is a one-to-one correspondence between uniformly bounded holomorphic functions of n complex variables in sectors of ℂⁿ, and uniformly bounded functions of n+1 real variables in sectors of that are monogenic functions in the sense of Clifford analysis. The result is applied to the construction of functional calculi for n commuting operators, including the example of differentiation operators on a Lipschitz surface in .