Showing papers in "Studia Mathematica in 1997"

Complementation in spaces of symmetric tensor products and polynomials

Abstract: Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].

Moment inequalities for sums of certain independent symmetric random variables

Abstract: This paper gives upper and lower bounds for moments of sums of independent random variables (Xk) which satisfy the condition that P (|X|k ≥ t) = exp(−Nk(t)), where Nk are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which N(t) = |t| for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N .

Distribution and rearrangement estimates of the maximal function and interpolation

Abstract: There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderon-Zygmund decomposition. Analogous methods allow us to obtain K-functional formulas in terms of the maximal function for couples of weighted $L_p$-spaces.

On Equivalemce of K- and J-Methods for (n+1)-Tuples of Banach Spaces

Abstract: It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices or their retracts. In general, these problems have negative solutions.

Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

Abstract: We prove that for every infinite-dimensional Banach space X with a Frechet differentiable norm, the sphere S-X is diffeomorphic to each closed hyperplane in X. We also prove that every infinite-dimensional Banach space Y having a (not necessarily equivalent) C-p norm (with p is an element of N boolean OR {infinity}) is C-p diffeomorphic to Y \ {0}.

A restriction theorem for the Heisenberg motion

Abstract: We prove a restriction theorem for the class-1 representations of the Heisenberg motion group. This is done using an improvement of the restriction theorem for the special Hermite projection operation operators proved in [13]. We also prove a restriction theorem for the Heisenberg group.