Transformations of differentiable functions
Transport equations with partially velocities
We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem where is the vector fieldwith a boundedness condition on the divergence of each vector field . This model was studied in the paper [LL] with a regularity assumption replacing our hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...
Triangular maps with the chain recurrent points periodic.
Turbulent maps and their ω-limit sets
One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Two classes of Darboux-like, Baire one functions of two variables
Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.
Two constructions of the real numbers via alternating series.
Two convergence theorems for Henstock-Kurzweil integrals and their applications to multiple trigonometric series
We establish two new norm convergence theorems for Henstock-Kurzweil integrals. In particular, we provide a unified approach for extending several results of R. P. Boas and P. Heywood from one-dimensional to multidimensional trigonometric series.
Two kinds of chaos and relations between them.
Two large subsets of a functional space.
Two mappings associated with Jensen's inequality.
Two Propositions On Slowly Varying Functions
Two theorems on measurable sets and sets having the Baire property
Two weight norm inequalities for fractional one-sided maximal and integral operators
In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: where and . We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral .
Two weight norm inequality for the fractional maximal operator and the fractional integral operator.
New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 < p < ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.
Two-weight norm inequalities for the rough fractional integrals.
Two-weighted criteria for integral transforms with multiple kernels
Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.
Typical continuous function without cycles is stable
Typical Dimension of the Graph of Certain Functions.
Typical measurable function in the topology of close approximation.
Typical sets and typical continuous functions