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This paper introduces some notions of e ective dimension for weighted function spaces. A space has low e ective dimension if the smallest ball in it that contains a function of variance 1, has no fu...
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ...
A rather complete investigation of anisotropic Bessel potential, Besov, and H\"older spaces on cylinders over (possibly) noncompact Riemannian manifolds with boundary is carried out. The geometry of t...
Abstract: We present new sharp assertions concerning multipliers in various spaces of harmonic functions in the unit ball of $R^n$.
The Gel’fand-Shilov spaces of type S are considered as topological algebras with respect to the Moyal star product and their corresponding algebras of multipliers are defined and investigated.
For a non-isolated point x of a topological space X let nw(x) be the smallest cardinality of a family N of infinite subsets of X such that each neighborhood O(x)  X of x contains a set N 2 N.
We survey research on the homotopy theory of the space map(X, Y )consisting of all continuous functions between two topological spaces. We summarize progress on various classification problems for the...
We study the superposition operators (also called Nemytskii operators) between spaces of almost periodic functions with values in a complete metric space or in a Banach space. We establish new resul...
In this paper, we investigate a linear homeomorphism between function spaces Cp(X) and Cp,A(X) \times Cp(A) , where X is a normal space and A is a neighborhood retraction of X.

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