Some observations on Besov and Lizorkin-Triebel spaces.
Some orthogonal decompositions of Sobolev spaces and applications
Two kinds of orthogonal decompositions of the Sobolev space W̊₂¹ and hence also of for bounded domains are given. They originate from a decomposition of W̊₂¹ into the orthogonal sum of the subspace of the -solenoidal functions, k ≥ 1, and its explicitly given orthogonal complement. This decomposition is developed in the real as well as in the complex case. For the solenoidal subspace (k = 0) the decomposition appears in a little different form. In the second kind decomposition the -solenoidal...
Some problems of global analysis on asymptotically simple manifolds
Some properties of weighted Sobolev spaces in
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 remarks about a notion of rearrangement
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 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 spaces of Morrey type.
Some remarks on strong approximation by Cesàro means
Some remarks on the characterization of the space of tangential traces of H(rot; ...) and the construction of an extension operator.
Some remarks on the density of regular mappings in Sobolev classes of SM-valued functions.
Some remarks on Triebel spaces
Some remarks on variational problems for functionals with growth
Some results on function spaces of varying smoothness
This paper deals with function spaces of varying smoothness , where the function :x ↦ s(x) determines the smoothness pointwise. Those spaces were defined in [2] and treated also in [3]. Here we prove results about interpolation, trace properties and present a characterization of these spaces based on differences.
Spaces of functions of generalized bounded variation. II: Questions of uniform convergence of Fourier series.
Spaces of functions on domain , whose -th derivatives are measures defined on