We observe that a separable Banach space is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if is not reflexive for reflexive and then is is not reflexive for some , having a basis.
It is shown that an orthonormal wavelet basis for associated with a multiresolution is an unconditional basis for , 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.
This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.
Let be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with , and denoted by . We show how properties of are transferred into properties of . Applications are given in multifractal analysis.
We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.
It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of...