Schatten Class Hankel Operators on the Harmonic Bergman Space of the Unit Ball

We give a necessary and sufficient condition for Hankel operators H_f on the harmonic Bergman space of the unit ball to be in the Schatten p-class for 2 ≤ p < ∞. A special case when symbol f is a harmonic function is also considered.     

Behavior of the Bergman Kernel Near Smooth Convex Boundary Points

The nontangential behavior of the Bergman metric near a smooth convex boundary point of a bounded pseudoconvex domain D ⁿ is studied in terms of its multitype.Received January 25, 2002; in revised form June 20, 2002 Published online November 18, 2002     

Propriétés diophantiennes du développement en cotangente continue de Lehmer

Diophantine Properties of Lehmer’s Continued Cotangent Developments. This article deals with an algorithm devised by Lehmer which enables us to write any real positive number as the sum of an alternating series of cotangents of integers n _ν, ν ≥ 0, in a unique way. We continue the work begun by Lehmer and continued by Shallit: amongst other things, we give explicitly the link between the rational approximations of a given real number coming from this algorithm and the usual convergents of the same real number and we produce a quasi-optimal bound for the growth of the sequence (n _ν)_{ν ≥ 0} associated to an algebraic number. We also determine the regular continued fractions of an exceptional class of continued cotangent developments, which enables us to produce optimal irrationality measures of these expansions.     

On Subspaces and Quotients of Banach Spaces C(K, X)

 We study the relation of to the subspaces and quotients of Banach spaces of continuous vector-valued functions , where K is an arbitrary dispersed compact set. More precisely, we prove that every infinite dimensional closed subspace of totally incomparable to X contains a copy of complemented in . This is a natural continuation of results of Cembranos-Freniche and Lotz-Peck-Porta. We also improve our result when K is homeomorphic to an interval of ordinals. Next we show that complemented subspaces (resp., quotients) of which contain no copy of are isomorphic to complemented subspaces (resp., quotients) of some finite sum of X. As a consequence, we prove that every infinite dimensional quotient of which is quotient incomparable to X, contains a complemented copy of . Finally we present some more geometric properties of spaces. Received 8 November 2000; in revised form 7 December 2001     

Orthogonal decompositions of Sobolev spaces in Clifford analysis

The space L ₂(G;ℂ _m ) of Clifford-algebra-valued functions in bounded domains G of ℝ ^m is decomposed into the orthogonal sum of the subspace of poly-left-monogenic functions of arbitrary order k≥1 and its orthogonal complement and as well into the orthogonal sum of the subspace of polyharmonic functions of arbitrary order k≥1 and its orthogonal complement. The complementary subspaces are given explicitly. In the particular case m=2, complex functions are involved. Although this case has to be treated separately, the results are as before. The proofs are based on proper higher-order Cauchy–Pompeiu formulas and Green functions for powers of the Laplacian. Received: July 4, 2000; in final form: January 7, 2001?Published online: December 19, 2001     

New spaces of functions and hyperfunctions for Hankel transforms and convolutions

In this paper we study the Hankel transformation and convolution on certain spaces of entire functions and its dual that is a space of hyperfunctions and contains the (even)-Schwartz space S _e ′. We prove that the Hankel transform is an automorphism of . Also the Hankel convolutors of are investigated. Authors’ addresses: Jorge J. Betancor, Claudio Jerez and Lourdes Rodríguez-Mesa, Departamento de Análisis Matemático, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofísico Francisco Sánchez, s/n, 38271 La Laguna (Sta. Cruz de Tenerife), Espa?a; Sandra M. Molina, Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350 (7600), Mar del Plata, Argentina     

Chebyshev polynomials for operators

The problem of uniqueness of the Chebyshev polynomials for bounded linear operators on normed linear spaces is investigated. Herrn Professor Dr. Dr. h.c. Heinz K?nig zu seinem achtzigsten Geburtstag gewidmet     

Mean ergodicity of multiplication operators in weighted spaces of holomorphic functions

Multiplication operators in weighted Banach (and locally convex) spaces of functions holomorphic in the unit disc are well known. In this note we investigate the connection between power boundedness, mean ergodicity and uniform mean ergodicity of such operators. Received: 13 October 2008, Revised: 18 November 2008     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Some remarks on multilinear maps and interpolation

A multilinear version of the Boyd interpolation theorem is proved in the context of quasi-normed rearrangement-invariant spaces. A multilinear Marcinkiewicz interpolation theorem is obtained as a corollary. Several applications are given, including estimates for bilinear fractional integrals. Received January 31, 1999 / Accepted February 27, 2000 / Published online December 8, 2000     

On summing operators on JB*-triples

In this paper we introduce 2-JB^*-triple-summing operators on real and complex JB^*-triples. These operators generalize 2-C^*-summing operators on C^*-algebras. We also obtain a Pietsch's factorization theorem in the setting of 2-JB^*-triple-summing operators on JB^*-triples. Received: 18 December 2000     

On periodic solutions of even-order ordinary differential equations

Optimal in a certain sense sufficient conditions are given for the existence and uniqueness of ω-periodic solutions of the nonautonomous ordinary differential equation u ^(2m) =f(t,u,...,u ^(m-1) ), where the function f:ℝ×ℝ ^m →ℝ is periodic with respect to the first argument with period ω. Received: December 21, 1999; in final form: August 12, 2000?Published online: October 2, 2001     

Hankel Operators on Bergman Spaces of Tube Domains over Symmetric Cones

We present here some criteria for Schatten-Von Neumann class membership for the small Hankel operator on Bergman space A ²(T _Ω), when T _Ω is the tube over the symmetric cone Ω. The author would like to thank professor Aline Bonami for helpful advices.     

Banach Spaces Admitting a Separating Polynomial and L P Spaces

 We prove that in a Banach space admitting a separating polynomial, each weakly null normalized sequence has a subsequence which is equivalent to the usual basis of some , p an even integer. We show that for each even integer p, the Schatten class admits a separating polynomial. For a space with a basis admitting a 4-homogeneous separating polynomial, we relate the unconditionality of the basis with the existence of certain type of polynomials defined in terms of infinite symmetric matrices. We find relations between the properties of the entries of these matrices and the geometrical structure of the space. Finally we study the existence of convex 4-homogeneous separating polynomials. Received 3 January 2001     

The overdetermined Cauchy problem in some classes of ultradifferentiable functions

In this paper we study the Cauchy problem for overdetermined systems of linear partial differential operators with constant coefficients in some spaces of ultradifferentiable functions of class (M _p ). We show that evolution is equivalent to the validity of a Phragmén-Lindel?f principle for entire and plurisubharmonic functions on some irreducible affine algebraic varieties, and make applications in different situations. We find necessary and sufficient conditions for well posedness, and relate the hyperbolicity of a given system to that of its principal part. Received: January 19, 1999?Published online: May 10, 2001     

Quasihyperbolic boundary conditions and Poincaré domains

We prove that a domain in whose quasihyperbolic metric satisfies a logarithmic growth condition with coefficient is a (q,p)-\Poincare domain for all p and q satisfying and , where denotes the Sobolev conjugate exponent. An elementary example shows that the given ranges for p and q are sharp. The proof makes use of estimates for a variational capacity. When p=2 we give an application to the solvability of the Neumann problem on domains with irregular boundaries. We also discuss the relationship between this growth condition on the quasihyperbolic metric and the s-John condition. Received: 2 May 2000 / Published online: 17 June 2002     

Unconditionality in spaces of smooth functions

Our main result shows that subspaces of L¹([0, 1]) on which the blow-up operators act compactly are isometric to dual spaces, and their natural predual belongs to the Banach-Mazur closure of quotient spaces of . Related general results are shown for subspaces X of or of reflexive K?the function spaces, which imply that when X consists of smooth functions it embeds into a Banach space with an unconditional basis. Received: 25 September 2008