Solid Hulls Research Articles

Solid hulls and cores of classes of weighted entire functions defined in terms of associated weight functions

In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming from weight sequences. These sequences are required to satisfy certain (standard) growth and regularity properties which are frequently arising and used in the theory of ultradifferentiable and ultraholomorphic function classes (where also the associated weight function plays a prominent role). Thanks to this additional information we are able to see which growth behavior the so-called ”Lusky-numbers”, arising in the representations of the solid hulls and cores, have to satisfy resp. if such numbers can exist.

Solid cores and solid hulls of weighted Bergman spaces

We determine the solid hull for 2<p<∞ and the solid core for 1<p<2 of weighted Bergman spaces Aμp,1<p<∞, of analytic functions on the disk and on the whole complex plane, for a very general class of nonatomic positive bounded Borel measures μ. New examples are presented. Moreover, we show that the space Aμp,1<p<∞, is solid if and only if the monomials are an unconditional basis of this space.

Solid hulls of weighted Banach spaces of entire functions

Given a continuous, radial, rapidly decreasing weight v on the complex plane, we study the solid hull of its associated weighted space H_v^\infty(\mathbb C) of all the entire functions f such that v|f| is bounded. The solid hull is found for a large class of weights satisfying the condition (B) of Lusky. Precise formulations are obtained for weights of the form v(r)= exp (-ar^p), a &gt; 0, p &gt; 0 . Applications to spaces of multipliers are included.

Solid hulls of weighted Banach spaces of analytic functions on the unit disc with exponential weights

The research of Bonet was partially supported by the projects MTM2013-43540-P and MTM2016-76647-P. This paper was completed during the Bonet's stay at the Katholische Universitat Eichstatt-Ingolstadt (Germany). The support of the Alexander von Humboldt Foundation is greatly appreciated. The research of Taskinen was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.

Influence of Cheaper Plant Media, Municipal Solid Waste Compost (MSWC) and Rice Hulls on Growth Characteristics of Pepper (Capsicum annuum L.) Seedlings

Peppers are used worldwide as spices, condiments and vegetables. Media incorporation of municipal solid waste compost (MSWC) and rice hulls usually results in a positive effect on the growth of a wide variety of crops. This study was carried out to measure the growth of pepper (Capsicum annuum L.) seedlings in five different levels of media mixtures (peat moss, rice hulls and MSWC). The measured traits were live plant percentage, number of leaf, plant height, shoot diameter, root length, shoot dry matter, root dry matter, plant ash, shoot fresh weight, root fresh weight, shoot dry weight and root dry weight. Analysis of variance (ANOVA) showed that different media mixture affected growth traits of pepper (except for essential oil yield and Shoot diameter). With decreasing of peat moss levels (100 to 60 v/v) the essential oil yields decreased. Results showed that increasing municipal solid waste compost increased almost growth of all traits. In the most of traits, the best result was observed with treatment 5 (peat moss 60 units, rice hulls 35 units and municipal solid waste compost 50 units v/v). Our study showed that increasing MSWC plus rice hulls in medium composition increased most plant traits growth and were benefit for growing pepper seedlings.

On the solid hulls of the Nevanlinna and Smirnov classes

In the paper, the solid and positive solid hulls of the Nevanlinna class and the Smirnov class of the unit disc are described. The result is applied to find the best possible estimations of the Taylor coefficients and the multipliers from the Smirnov class into some large spaces of holomorphic functions. These results provide a much “softer” and easier way to obtain even stronger results on the multipiers and the mean growth of the Taylor coefficients proved by Yanagihara.

Solid hulls of quasi-Banach spaces of analytic functions and interpolation

Abstract We study solid hulls of abstract Hardy spaces of analytic functions on the unit disk. Interpolation of sublinear operators is used to description of solid hulls of quasi-Banach spaces generated by interpolation methods associated to classical Hardy spaces H p for 0 p 1 . We specialize our results to solid hulls of Hardy–Orlicz and Hardy–Lorentz spaces and we are able to characterize multipliers from Hardy–Lorentz spaces to any solid sequence space. We give, for example, a complete description of multipliers with the domain in Hardy–Lorentz–Zygmund spaces.

On the solid hull of the Hardy-Lorentz space

The solid hulls of the Hardy-Lorentz spaces Hp,q,0 &lt; p &lt; 1, 0 &lt; q ? ? and Hp,? 0, 0 &lt; p &lt; 1, as well as of the mixed norm space H p,?,? 0,0 &lt; p ? 1, 0 &lt; ? &lt; ?, are determined.

Hull characteristics as related to susceptibility of different varieties of rough rice to Rhyzopertha dominica (F.) (Coleoptera: Bostrichidae)

Rhyzopertha dominica (F.), an important pest of stored grains, causes economic damage to rough rice through physical damage to the kernel, resulting in reductions in grain quality. In this test, 28 varieties of commercial rough rice (10 long grain, 11 medium grain, and 7 short grain) were examined for solid, split and cracked hulls, hull thickness, and adult emergence from neonate R. dominica introduced on each individual variety. The percentage of solid hulls ranged from 55.5% on Koshihikari variety to 92.8% on Akita variety, and the percentages of cracked and split hulls were correlated with increased susceptibility. The Dobie index for progeny production showed Wells, Jupiter, and Pirogue varieties as the most tolerant to R. dominica, while Rico and Francis were the most susceptible. The hull thickness of rough rice varied among varieties, but the tolerant varieties appeared to have thicker hulls than the susceptible varieties. There was no difference among rice types (long-, medium-, or short grain) regarding tolerance or susceptibility to R. dominica. Results show that the characteristics of the rough rice hull are important for conferring susceptibility of individual varieties to R. dominica.

On Some Topological Properties of Vector-Valued Function Spaces

Let E be an ideal of L0 over a σ-finite measure space (Ω,Σ, μ) with a Hausdorff locally convex-solid topology ξ, and let (X, ‖ · ‖X) be a real Banach space. Let E(X) be a subspace of the space L0(X) of μ-equivalence classes of all strongly Σ-measurable functions f : Ω → X and consisting of all those f ∈ L0(X) for which the scalar function ‖f(·)‖X belongs to E. In this paper we show that a number of topological properties of the spaces X and (E, ξ) can be lifted to the space (E(X), ξ), where ξ stands for the topology on E(X) associated with ξ. We characterize some important topological properties of the space (E(X), ξ) (weak compactness of order intervals, almost reflexivity, weak sequential completeness, semi-reflexivity, relative weak compactness of solid hulls) in terms of the corresponding properties of X and (E, ξ).

Constructions of Solid Hulls

For each concrete category (K,U) an extension LIM(K,U) is constructed and under certain 'smallness conditions' it is proved that LIM(K,U) is a solid hull of (K,U), i.e., the least finally dense solid extension of (K,U). A full subcategory of Top2 is presented which does not have a solid hull.

Relative weak compactness of solid hulls in Banach lattices

We show that the solid hull of every relatively weakly compact set in a Banach lattice is again relatively weakly compact if and only if the Banach lattice is an order direct sum of a KB-space and an atomic Banach lattice with an order continuous norm. If we assume order continuity of the norm then this is equivalent to requiring that the image of every relatively weakly compact set under the modulus map is again relatively weakly compact. We also show that amongst Banach lattices with an order continuous norm those that have the property that the lattice operations are weakly sequentially continuous are precisely the atomic ones. The final section of the paper is devoted to applications of our earlier results to questions concerning the factorization of compact and weakly compact operators through reflexive Banach lattices.

Solid hulls of concrete categories

This paper deals with the problem of the existence of solid hulls for concrete categories. We present sufficient conditions for a concrete category to have a solid hull. For concrete categories over Set with a small finally dense subcategory, we observe that the existence of solid hulls is equivalent to Weak Vopenka's Principle.