Weak solutions of degenerated quasilinear elliptic equations of higher order.
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 continuity and weak sequential continuity of continuous n-linear mappings between Banach spaces.
In this paper it is shown that the class LnWU (E1,E2,...,En;F) of weakly uniformly continuous n-linear mappings from E1x E2x...x En to F on bounded sets coincides with the class LnWSC (E1,E2,...,En;F) of weakly sequentially continuous n-linear mappings if and only if for every Banach space F, each Banach space Ei for i = 1,2,...,n does not contain a copy of l1.
Weak uniform rotundity in Orlicz spaces
Weak*-Dense Subspaces of Loo (R).
Weakly almost periodic vector-valued functions [Book]
Weakly compact composition operators on analytic vector-valued function spaces.
Weakly Compact Operators and the Dunford-Pettis Property on Uniform Spaces
Weakly compact operators and -additive measures
Weakly compact operators from a B-space into the space of Bochner integrable functions
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 ...
Weakly continuous functions of Baire class 1.
For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
Weakly precompact subsets of L₁(μ,X)
Let (Ω,Σ,μ) be a probability space, X a Banach space, and L₁(μ,X) the Banach space of Bochner integrable functions f:Ω → X. Let W = f ∈ L₁(μ,X): for a.e. ω ∈ Ω, ||f(ω)|| ≤ 1. In this paper we characterize the weakly precompact subsets of L₁(μ,X). We prove that a bounded subset A of L₁(μ,X) is weakly precompact if and only if A is uniformly integrable and for any sequence (fₙ) in A, there exists a sequence (gₙ) with for each n such that for a.e. ω ∈ Ω, the sequence (gₙ(ω)) is weakly Cauchy in X....
Weakly sufficient sets for A-∞(D).
In the space A-∞(D) of functions of polynomial growth, weakly sufficient sets are those such that the topology induced by restriction to the set coincides with the topology of the original space. Horowitz, Korenblum and Pinchuk defined sampling sets for A-∞(D) as those such that the restriction of a function to the set determines the type of growth of the function. We show that sampling sets are always weakly sufficient, that weakly sufficient sets are always of uniqueness, and provide examples...
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 , .
Weierstrass' theorem in weighted Sobolev spaces with derivatives: announcement of results.
Weierstrass transform associated with the Hankel operator.