Tent space boundedness via extrapolation

Allowed Patterns of Symmetric Tent Maps via Commuter Functions

We introduce a new technique to study pattern avoidance in dynamical systems, namely the use of a commuter function between non-conjugate dynamical systems. We investigate the properties of such a commuter function, specifically h : [0, 1]→ [0, 1] satisfying T1 ◦ h = h ◦ Tμ, where Tμ denotes a symmetric tent map of height μ. We make use of this commuter function to prove strict inclusion of the...

On the Range Space of Yano’s Extrapolation Theorem and New Extrapolation Estimates at Infinity

o-Boundedness of free objects over a Tychonoff space

In this paper we characterize various sorts of boundedness of the free (abelian) topological group F (X) (A(X)) as well as the free locally-convex linear topological space L(X) in terms of properties of a Tychonoff space X. These properties appear to be close to so-called selection principles, which permits us to show, that (it is consistent with ZFC that) the property of Hurewicz (Menger) is l...

Boundedness and Compactness of Operators on the Fock Space

We obtain sufficient conditions for a densely-defined operator on the Fock space to be bounded or compact. Under the boundedness condition we then characterize the compactness of the operator in terms of its Berezin transform.

Control Functions and Total Boundedness in the Space L0

In this paper we introduce a parameter ω∞ in the space of functions L0. The parameter measures the lack of equimeasurability using a sequence of functions which controls the oscillations of every function of a given subset of L0. We estimate the Hausdorff measure of noncompactness in terms of ω∞ and the parameter σ (see [3]) and characterize the totally bounded subsets of L0. A criterion of com...