Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

Functions related to convexity and smoothness of normed spaces

We introduce a few functions related to convexity and smoothness of normed spaces. Those functions turn out to be moduli of convexity or smoothness or play an intermediate role. We calculate the exact formulas for introduced functions in some classical Banach spaces. An application to geometry of normed spaces is also indicated.     

On the smoothness of the moduli space of mathematical instanton bundles

In this paper we prove that the moduli spaces MI _2n+1(k) of mathematical instanton bundles on ²ⁿ⁺¹ with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993.     

A difference between continuous and absolutely continuous norms in Banach function spaces

On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.     

On integration in complete bornological locally convex spaces

A generalization of I. Dobrakov's integral to complete bornological locally convex spaces is given.     

The Symmetry of 2-Flat Homogeneous Spaces

A Riemannian manifold M is called 2-flat homogeneous if every geodesic is contained in some 2-flat , and if the group of isometries of M acts transitively on the set of pairs (p, ) with p . By a 2-flat we mean a closed, connected, flat, totally geodesic, 2-dimensional submanifold of M. It is proved in the paper that 2-flat homogeneous spaces are symmetric.     

Embedding the Linear Structure of Planar Spaces into Projective Spaces

We show that every non-degenerate planar space with v points and planes can be embedded as a linear space into PG(3,q) for some prime power q provided that 1000( - v) v^5/6;     

Λ0-Nuclear Operators and Λ0-Nuclear Spaces in p-adic Analysis

For a Köthe sequence space, the classes of ₀-nuclear spaces and spaces with the ₀-property are introduced and studied and the relation between them is investigated. Also, we show that, for ₀c ₀, these classes of spaces are in general different from the corresponding ones for ₀=c ₀, which have been extensively studied in the non-archimedean literature (see, for example, [1]–[6]).