Search results for "Predual"
showing 3 items of 3 documents
Atomic Decomposition of Weighted Besov Spaces
1996
We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…
Preduals of spaces of homogeneous polynomials onLp-spaces
2012
Given a regular probability measure μ on a compact Hausdorff space, we explicitly describe the predual of the Banach space of continuous n-homogeneous polynomials on L p (μ) as the completion of a (explicit constructed) subspace of L p/n (μ) with respect to a (explicitly constructed) norm π p/n . An application to the factorization of dominated polynomials is provided.
Quasi-Normable Preduals of Spaces of Holomorphic Functions
1997
Abstract Let H ( U ) denote the space of all holomorphic functions on an open subset U of a separable Frechet space E . Let τ ω denote the compact-ported topology on H ( U ) introduced by Nachbin. Let G ( U ) denote the predual of H ( U ) constructed by Mazet. In our main result we show that E is quasi-normable if and only if G ( U ) is quasi-normable if and only if ( H ( U ), τ ω ) satisfies the strict Mackey convergence condition.