INTERPOLATION SPACES BETWEEN H^1 AND L^∞ ON SPACES OF HOMOGENEOUS TYPE

Using the maximal function characterization of Hardy spaces,we study the interpolation spaces between H^1 and L^∞on spaces of homogeneous type.     

Complex contact manifolds and S1 actions

We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a curvature condition.     

Hyperbolic principal cycles on hypersurfaces ofIR4

The topological structure of lines of curvature of hypersurfaces ofIR ⁴ around principal cycles is studied in this work. Given a principal cycle we show how to hyperbolize it with a small deformation of the immersion.     

Sequences of minimal surfaces in S2n+1

For a minimal surface immersed into an odd-dimensional unit sphere S ²ⁿ⁺¹ with the first (n−2) higher-order ellipses of curvature being a circle, we construct a sequence of such surfaces and investigate if some two minimal surfaces in such a sequence can be congruent by an orientation-reversing isometry.     

Interpolation problems on the spectrum of H∞

We characterize those sequences (x _n ) in the spectrum of H ^∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f _n (x) for every x ∈ P(x _n ), where P(x _n ) is the Gleason part associated with the point x _n and where (f _n ) is an arbitrary sequence of functions in the unit ball of H ^∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions, a result first proved by Gallardo and Gorkin.     

The automorphism group of the Toeplitz algebra onH2(T2)

The automorphism group of the C^* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .     

Relative K homology and C* algebras

Let A be a separable nuclear C ⁺ algebra with unit. Let be a closed two-sided ideal in A. A relative K homology group K ⁰(A,) is defined. Closely related are topological definitions of properly supported K homology and of compactly supported relative K homology. Applications are to indices of Toeplitz operators and existence of coercive boundary conditions for elliptic differential operators.     

Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

Boundedness of Marcinkiewicz integrals and their commutators in H1 (?n × ?m)

The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H ¹ (ℝ ⁿ × ℝ ^m ) to the Lebesgue space L ¹(ℝ ⁿ × ℝ ^m ) and their commutators with Lipschitz functions from the Hardy space H ¹ (ℝ ⁿ × ℝ ^m ) to the Lebesgue space L ^q (ℝ ⁿ × ℝ ^m ) for some q > 1.     

ltivariate Hausdorff operators on the spaces H1(Rn) and BMO(Rn)

Summary A multivariate Hausdorff operator H = H(, c, A) is defined in terms of a -finite Borel measure on Rⁿ, a Borel measurable function c on Rⁿ, and an n × n matrix A whose entries are Borel measurable functions on rⁿ and such that A is nonsingular -a.e. The operator H*:= H (, c | det A^-1|, A^-1) is the adjoint to H in a well-defined sense. Our goal is to prove sufficient conditions for the boundedness of these operators on the real Hardy space H¹(Rⁿ) and BMO (Rⁿ). Our main tool is proving commuting relations among H, H*, and the Riesz transforms R_j. We also prove commuting relations among H, H*, and the Fourier transform.     

Holomorphic map with unipotent jacobian matrices in C3

We prove that the holomorphic unipotent Jacobian conjecture is valid when n = 3.     

Quasi-permutation Representations of the Groups SU (3, q2) and PSU (3, q2)

A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU (3, q²) and SU (3, q²).AMS Subject Classification (2000): 20C15