Wavelet bases in
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.
Wavelet techniques for pointwise regularity
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.
Wavelets as Unconditional Bases in L...(...).
Weak and extra-weak type inequalities for the maximal operator and the Hilbert transform
Weak bounds for the maximal function in weighted Orlicz spaces
Weak Cauchy sequences in
For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of is discussed.
Weak compactness and Orlicz spaces
We give new proofs that some Banach spaces have Pełczyński's property (V).
Weak compactness criteria and convergences in LE1(μ).
Weak convergence and weighted averages for groups of operators
Weak orthogonality and weak property () in some Banach sequence spaces
It is proved that a Köthe sequence space is weakly orthogonal if and only if it is order continuous. Criteria for weak property () in Orlicz sequence spaces in the case of the Luxemburg norm as well as the Orlicz norm are given.
Weak type inequalities for the maximal ergodic function and the maximal ergodic Hilbert transform in weighted spaces
Weak type radial convolution operators on free groups
Radial convolution operators on free groups with nonnegative kernel of weak type (2,2) and of restricted weak type (2,2) are characterized. Estimates of weak type (p,p) are obtained as well for 1 < p < 2.
Weak uniform rotundity in Orlicz spaces
Weak*-Dense Subspaces of Loo (R).
Weakly compact operators on Köthe-Bochner spaces with the mixed topology
Let E be a Banach function space and let X be a real Banach space. We examine weakly compact linear operators from a Köthe-Bochner space E(X) endowed with some natural mixed topology (in the sense of Wiweger) to a Banach space Y.
Weakly compact sets in Orlicz sequence spaces
We combine the techniques of sequence spaces and general Orlicz functions that are broader than the classical cases of -functions. We give three criteria for the weakly compact sets in general Orlicz sequence spaces. One criterion is related to elements of dual spaces. Under the restriction of , we propose two other modular types that are convenient to use because they get rid of elements of dual spaces. Subsequently, by one of these two modular criteria, we see that a set in Riesz spaces ...
Weak-star density of polynomials.
Weak-type inequalities for maximal operators acting on Lorentz spaces
We prove sharp a priori estimates for the distribution function of the dyadic maximal function ℳ ϕ, when ϕ belongs to the Lorentz space , 1 < p < ∞, 1 ≤ q < ∞. The approach rests on a precise evaluation of the Bellman function corresponding to the problem. As an application, we establish refined weak-type estimates for the dyadic maximal operator: for p,q as above and r ∈ [1,p], we determine the best constant such that for any , .
Weight inequalities for singular integrals defined on spaces of homogeneous and nonhomogeneous type.
Weighted composition operators between spaces of Dirichlet type.