A weak invertibility criterion in the weighted -spaces of holomorphic functions in the ball.
A weak molecule condition for certain Triebel-Lizorkin spaces
A weak molecule condition is given for the Triebel-Lizorkin spaces Ḟ_p^{α,q}, with 0 < α < 1 and 1 < p, q < ∞. As an easy corollary, one may deduce, by atomic-molecular methods, a Triebel-Lizorkin space "T1" Theorem of Han and Sawyer, and Han, Jawerth, Taibleson and Weiss, for Calderón-Zygmund kernels K(x,y) which are not assumed to satisfy any regularity condition in the y variable.
A Whitney extension theorem in and Besov spaces
The classical Whitney extension theorem states that every function in Lip, , closed, , a non-negative integer, can be extended to a function in Lip. Her Lip stands for the class of functions which on have continuous partial derivatives up to order satisfying certain Lipschitz conditions in the supremum norm. We formulate and prove a similar theorem in the -norm.The restrictions to , , of the Bessel potential spaces in and the Besov or generalized Lipschitz spaces in have been...
A Тote on the Сompleteness of
A₁-regularity and boundedness of Calderón-Zygmund operators
The Coifman-Fefferman inequality implies quite easily that a Calderón-Zygmund operator T acts boundedly in a Banach lattice X on ℝⁿ if the Hardy-Littlewood maximal operator M is bounded in both X and X'. We establish a converse result under the assumption that X has the Fatou property and X is p-convex and q-concave with some 1 < p, q < ∞: if a linear operator T is bounded in X and T is nondegenerate in a certain sense (for example, if T is a Riesz transform) then M is bounded in both X and...
Abelian ergodic theorems for contraction semigroups
About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.
About an example of a Banach space not weaky K-analytic.
About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system.
About projections of logarithmic Sobolev inequalities
Absolute bases, tensor products and a theorem of Bohr
Absolute continuity of the Sobolev type functions on metric spaces.
Absolutely continuous linear operators on Köthe-Bochner spaces
Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let and be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.
Absolutely (∞,p) summing and weakly-p-compact operators in C(K).
In this note we review some results about:1. Representation of Absolutely (∞,p) summing operators (∏∞,p) in C(K,E)2. Dunford-Pettis properties.
Abstract characterization of Orlicz-Kantorovich lattices associated with an -valued measure
An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.
Abstract Korovkin-type theorems in modular spaces and applications
We prove some versions of abstract Korovkin-type theorems in modular function spaces, with respect to filter convergence for linear positive operators, by considering several kinds of test functions. We give some results with respect to an axiomatic convergence, including almost convergence. An extension to non positive operators is also studied. Finally, we give some examples and applications to moment and bivariate Kantorovich-type operators, showing that our results are proper extensions of the...
Adams inequality on metric measure spaces.
Adaptive Deterministic Dyadic Grids on Spaces of Homogeneous Type
In the context of spaces of homogeneous type, we develop a method to deterministically construct dyadic grids, specifically adapted to a given combinatorial situation. This method is used to estimate vector-valued operators rearranging martingale difference sequences such as the Haar system.
Addendum to “Curves of maximum modulus in coherent state representations”
Addendum to "Lineability and spaceability of vector-measure spaces" (Studia Math. 219 (2013), 155-161)