Note on hit-and-miss topologies

This is a continuation of [19]. We characterize first and second countability of the general hit-and-miss hyperspace topologyτ ₊ ^Δ for weakly-R ₀ base spaces. Further, metrizability ofτ ₊ ^Δ is characterized with no preliminary conditions on the base space and the generating family of closed sets and a new proof on uniformizability (i.e. complete regularity) ofτ ₊ ^Δ is given in this general setting, thus generalizing results of [3], [5] and [6].     

Dwork cohomology and algebraic ${\Cal D}$-modules

Using local cohomology and algebraic -Modules, we generalize a comparison theorem between relative de Rham cohomology and Dwork cohomology due to N. Katz, P. Monsky, A. Adolphson and S. Sperber. Received June 10, 1999 / Published online July 20, 2000     

An extension of Hawkes theorem on the Hausdorff dimension of a Galton–Watson tree

Let ? be the genealogical tree of a supercritical multitype Galton–Watson process, and let Λ be the limit set of ?, i.e., the set of all infinite self-avoiding paths (called ends) through ? that begin at a vertex of the first generation. The limit set Λ is endowed with the metric d(ζ, ξ) = 2 ⁻ⁿ where n = n(ζ, ξ) is the index of the first generation where ζ and ξ differ. To each end ζ is associated the infinite sequence Φ(ζ) of types of the vertices of ζ. Let Ω be the space of all such sequences. For any ergodic, shift-invariant probability measure μ on Ω, define Ω_μ to be the set of all μ-generic sequences, i.e., the set of all sequences ω such that each finite sequence v occurs in ω with limiting frequency μ(Ω(v)), where Ω(v) is the set of all ω′?Ω that begin with the word v. Then the Hausdorff dimension of Λ∩Φ⁻¹ (Ω_μ) in the metric d is

The essential norm of Hankel operator on the Bergman spaces of strongly pseudoconvex domains

Let D be a bounded strongly pseudoconvex domain with smooth boundary in Cⁿ and let fL²(D). For the Hankel operator H_f on the Bergman space A²(D), it is shown that the essential norm of H_f in L²(D) is comparable to the distance norm from H_f to compact Hankel operators. The result extends the previous corresponding version in the disc proved by Lin and Rochberg in Integ.Equat.Oper.Theory 361–372,17 (1993).     

Quadratically hyponormal weighted shifts with two equal weights

We present an extensive analysis ofpositively quadratically hyponormal weighted shiftsW with ₀ = ₁ = 1. Our main result states that such weighted shifts abound! Specifically, by focusing on recursively generated weighted shifts of the form, we establish that the planar set is positively quadratically hyponormal} is a closed convex, set with nonempty interior. In addition, we are able to describe in detail the boundary of Research partially supported by NSF grants DMS-9401455 and DMS-9800931Research partially supported by KOSEF grant 971-0102-006-2 and by TGRC-KOSEF     

Hyperinvariant subspaces ofC 0-operators over a multiply connected region

In this paper we find a relation between the lattice of hyperinvariant subspaces of an operatorT of classC ₀ over a multiply connected region and that of its Jordan modelT. It is shown that, generally, the lattice corresponding toT can be identified with a retract of that corresponding toT. Thus the Jordan model has the smallest lattice of hyperinvariant subspaces in a given quasisimilarity class.     

Smallest g -supersolution with constraint

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition. Then by considering (ξ, g) as a parameter of BSDE, and (ξ ^α, g ^α) as a class of parameters for BSDE, where α belongs to a set , for every there exists a pair of solution {Y ^a, Z^a} for the BSDE, the properties of which is also a solution for some BSDE is studied. This result may be used to discuss optimal problems with recursive utility. This work was supported by NSFC (79790130)     

A note on regularity for a class of quasilinear elliptic equations

The following regularity of weak solutions of a class of elliptic equations of the form are investigated.     

On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.     

The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.