On the unique finite (SI) decomposition of the Jordan operator ⊕ i=1 n S(θ) for certain inner function θ

In this paper, we have proven that for the Jordan blockS() withS() (SI), _i=1 ⁿ S() =S() ⁽ⁿ⁾ (n 1) has unique finite (SI) decomposition up to a similarity. As result, we obtain that ifV is a Volterra operator onH=L ²([0, 1]), thenV ⁽ⁿ⁾ has unique finite (SI) decomposition.This project was supported by National Natural Science Foundation of China.     

The boundedness below of 2×2 upper triangular operator matrices

Wen and are given we denote byM _C an operator acting on the Hilbert space of the form

Bounds on leaves of one-dimensional foliations

Let X be a variety over an algebraically closed field, a onedimensional singular foliation, and a projective leaf of . We prove that

Random k-Sat: A Tight Threshold For Moderately Growing k

We consider a random instance I of k-SAT with n variables and m clauses, where k=k(n) satisfies k—log₂ n. Let m ₀=2 ^k nln2 and let =(n)>0 be such that n. We prove that

Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative

In this paper, we consider the following second-order three-point boundary value problem

Increasing Self-Described Sequences

We proceed with our study of increasing self-described sequences F, beginning with 1 and defined by a functional equation In [1] we exhibited the simple solution f (t)=Ct, for some (0,1), of the associated functional-differential equation and we proved that provided <2/(2+d()), where we have the asymtotic equivalence F(m)~ Cm.In the present paper we show that this last result is optimal, in the sense that the self-described sequence defined by |F^–1(m)|=F(m)², that is

Quasi-linear parabolic problems in L 1 with non homogeneous conditions on the boundary

We are interested in parabolic problems with L¹ data of the type

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

The normal density of prime ideals in small regions

For a Gaussian prime (i) define ()=min|–| where runs through Gaussian primes satisfying ||>||. We prove that, subject to the Riemann Hypothesis for appropriateL-functions

Comments on the Trotter product formula error-bound estimates for nonself-adjoint semigroups

LetA be a positive self-adjoint operator and letB be anm-accretive operator which isA-small with a relative bound less than one. LetH=A+B, thenH is well-defined on dom(H)=dom(A) andm-accretive. IfB is a strictlym-accretive operator obeying

Generalized solution to a semilinear hyperbolic system with a non-Lipshitz nonlinearity

Let

Some remarks on the product of two C α-compact subsets

For a cardinal , we say that a subset B of a space X is C -compact in X if for every continuous function is a compact subset of . If B is a C-compact subset of a space X, then (B, X) denotes the degree of C -compactness of B in X. A space X is called -pseudocompact if X is C -compact into itself. For each cardinal , we give an example of an -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in Some cardinal generalizations of pseudocompactness Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg's Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases.     

On local oscillatory integrals with variable Calderón-Zygmund kernels

Letp(1, ). In this paper, the authors investigate the uniformL ^p ( ⁿ ) in of the oscillatory singular integral operatorT defined by

On very weak entire solutions of nonlinear partial differential equations

Let us consider the variational equation in R ⁿ

Concentration phenomena in weakly coupled elliptic systems with critical growth*

In this paper we consider the weakly coupled elliptic system with critical growth

The convolution equation of Choquet and Deny on [IN]-groups

Let be a probability measure on a locally compact groupG. A real Borel functionf onG is called -harmonic if it satisfies the convolution equation *f=f. Given that isnonsingular with its translates, we show that the bounded -harmonic functions are constant on a class of groups including the almost connected [IN]-groups. If is nondegenerate and absolutely continuous, we solve the more general equation *= for positive measure on those groups which are metrizable and separable.Supported by Hong Kong RGC Earmarked Grant and CUHK Direct Grant     

On Some Isomorphism on the Category of b-Spaces

Given a nuclear b-space N, we show that if is a finite or -finite measure space and 1p, then the functors L _loc ^p (,N.) and NL ^p (,.) are isomorphic on the category of b-spaces of L. Waelbroeck.     

On singular integrals along surfaces related to black spaces

Leth(t) be an arbitrary bounded radial function and let (x) be a real measurable and radial function defined onR ^n–1. Forx, yR ^n–1, we establish that the singular integral along surfacex (x, (x)):

Weighted norm inequalities for geometric fractional maximal operators

For 0 < let Tf denote one of the operators

On the Integrability of Eigenfunctions of the Laplace-Beltrami Operator in the Unit Ball of C n

Let B denote the unit ball in C ⁿ , n1, and let , , and denote the volume measure, gradient, and Laplacian respectively, with respect to the Bergman metric on B. For R and 0<p<, we denote by L ^p the set of real, or complex-valued measurable functions f on B for which _B (1–|z|²)|f(z)| ^p d(z)<, and by D ^p the Dirichlet space of C ¹ functions f on B for which | f|L ^p . Also, for C, we denote by X the set of C ² real, or complex-valued functions f on B for which f=f. The main result of the paper is as follows: Let 0<p< and suppose R with –n ². Then L ^p X ={0}, and for 0, D ^p X ={0}(a) for all n+ when p1, and(b) for all when 0<p<1.By example it is shown that the result is best possible for all values of p with pn/(n+ .