Some properties of weakly countably determined Banach spaces
Some properties of weighted Sobolev spaces in
Some properties on the closed subsets in Banach spaces
It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Some Ramsey type theorems for normed and quasinormed spaces
We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.
Some rationally convex sets
Some recent results concerning weak Asplund spaces
Some relations among volume, intrinsic perimeter and one-dimensional restrictions of functions in Carnot groups
Let be a -step Carnot group. The first aim of this paper is to show an interplay between volume and -perimeter, using one-dimensional horizontal slicing. What we prove is a kind of Fubini theorem for -regular submanifolds of codimension one. We then give some applications of this result: slicing of functions, integral geometric formulae for volume and -perimeter and, making use of a suitable notion of convexity, called-convexity, we state a Cauchy type formula for -convex sets. Finally,...
Some Relations Between Additive Functions - II
Some relations between Toeplitz and singular integral operators on odd spheres
Some remarkable lines of triangles in real normed spaces and characterizations of inner product structures.
Some remarks about a notion of rearrangement
Some remarks about Mackey convergence.
Some remarks about metric spaces, spherical mappings, functions and their derivatives.
If p ∈ Rn, then we have the radial projection map from Rn {p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a function in terms of its gradient, which can then be used to derive Sobolev inequalities, etc. In this paper...
Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type.
Some remarks about the density of smooth functions in weighted Sobolev spaces.
Some remarks about the three spaces problem in Banach algebras
Some remarks an interpolation of operators and Fourier coefficients
Some remarks on a class of weight functions
In this paper we obtain some results about a class of functions , where is an open set of , which are related to the distance function from a fixed subset . We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function .
Some remarks on almost radiality in function spaces
Some remarks on -Baire-like and --Baire-like spaces