Characterizations for the potential operators on Carleson curves in local generalized Morrey spaces

In this paper, we give a boundedness criterion for the potential operator { {\mathcal I} }^{\alpha } in the local generalized Morrey space L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the generalized Morrey space {M}_{p,\varphi }(\text{Γ}) defined on Carleson curves \text{Γ} , respectively. For the operator { {\mathcal I} }^{\alpha } , we establish necessary and sufficient conditions for the strong and weak Spanne-type boundedness on L{M}_{p,\varphi }^{\{{t}_{0}\}}(\text{Γ}) and the strong and weak Adams-type boundedness on {M}_{p,\varphi }(\text{Γ}) .

Nehari’s Theorem for Convex Domain Hankel and Toeplitz Operators in Several Variables

We prove Nehari’s theorem for integral Hankel and Toeplitz operators on simple convex polytopes in several variables. A special case of the theorem, generalizing the boundedness criterion of the Hankel and Toeplitz operators on the Paley–Wiener space, reads as follows. Let $\Xi = (0,1)^d$ be a $d$-dimensional cube, and for a distribution $f$ on $2\Xi $, consider the Hankel operator $$\Gamma_f (g)(x)=\int_{\Xi} f(x+y) g(y) \, dy, \quad x \in\Xi.$$ Then $\Gamma _f$ extends to a bounded operator on $L^2(\Xi )$ if and only if there is a bounded function $b$ on ${{\mathbb{R}}}^d$ whose Fourier transform coincides with $f$ on $2\Xi $. This special case has an immediate application in matrix extension theory: every finite multilevel block Toeplitz matrix can be boundedly extended to an infinite multilevel block Toeplitz matrix. In particular, block Toeplitz operators with blocks that are themselves Toeplitz can be extended to bounded infinite block Toeplitz operators with Toeplitz blocks.

Bounded sets of sheaves on Kähler manifolds

We show that any set of quotients with fixed Chern classes of a given coherent sheaf on a compact Kähler manifold is bounded in a sense which we define. The result is proved by adapting Grothendieck's boundedness criterion expressed via the Hilbert polynomial to the Kähler set-up. As a consequence we obtain the compactness of the connected components of the Douady space of a compact Kähler manifold.

Sõnajärg, infostruktuur ja objekti kääne eesti keeles

Objekti kääne eesti keeles oleneb eelkõige tegevuse ja objekti piiritle- (ma)tusest, kuid da-infinitiiviga konstruktsioonides leidub palju varieerumist objekti käändes, mida ei ole võimalik seletada piiritletuse mõiste abil. Suur osa sellest varieerumisest on seotud sõnajärjega: da-infinitiivile järgnev objekti on pigem totaalne, infinitiivile eelnev objekt on pigem partsiaalne. Artiklis vaadeldakse seoseid sõnajärje ja objekti käände vahel neljas sagedases da-infinitiiviga konstruktsioonis. Kuna eesti keele sõnajärg sõltub suuresti infostruktuurist, uuritakse, kas ja kuivõrd on sõnajärjega seotud varieerumine seletatav infostruktuuriliste parameetrite abil. Jõutakse järeldusele, et objekti käände varieerumist ei mõjuta mitte infostruktuur, vaid sõnajärg ise. Artikli lõpuosas arutletakse selle üle, miks võiks sõnajärg üldse mõjutada objekti käänet ning miks selle mõju piirdub infiniitsete konstruktsioonidega.Abstract. David Ogren: Word order, information structure and object case in Estonian. While object case in Estonian depends primarily on the boundedness of the action and the object nominal, numerous constructions with da-infinitive verb forms exhibit object case variation that cannot be explained by the boundedness criterion. A considerable amount of this variation is related to word order: VO word order in the da-infinitive phrase favors the use of the total object, OV word order favors the partial object. The article examines the relationship between word order and object case in four common da-infinitive constructions. As word order in Estonian is heavily dependent on information structure, the article also investigates whether the relationship between word order and object case can be explained by information-structural features, and finds that the relevant parameter is in fact not information structure, but rather word order itself. The article closes with a discussion of the possible explanations for the relationship between word order and object case and for why this relationship is found only in non-finite constructions.Keywords: object case, da-infinitive, information structure, word order, variation, analogy