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1.
If 0 < p < ∞ and α > − 1, the space
consists of those functions f which are analytic in the unit disc
and have the property that f ′ belongs to the weighted Bergman space Aαp. In 1999, Z. Wu obtained a characterization of the Carleson measures for the spaces
for certain values of p and α. In particular, he proved that, for 0 < p ≤ 2, the Carleson measures for the space
are precisely the classical Carleson measures. Wu also conjectured that this result remains true for 2 < p < ∞. In this paper we prove that this conjecture is false. Indeed, we prove that if 2 < p < ∞, then there exists g analytic in
such that the measure μg,p on
defined by dμg,p (z) = (1 − |z|2)p - 1| g ′ (z)|p dx dy is not a Carleson measure for
but is a classical Carleson measure. We obtain also some sufficient conditions for multipliers of the spaces
相似文献
2.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
相似文献
3.
A 1-factorization (or parallelism) of the complete graph with loops
is called polar if each 1-factor (parallel class) contains exactly one loop and for any three distinct vertices x1, x2, x3, if {x1} and {x2, x3} belong to a 1-factor then the same holds for any permutation of the set {1, 2, 3}. To a polar graph
there corresponds a polar involution set
, an idempotent totally symmetric quasigroup (P, *), a commutative, weak inverse property loop (P, + ) of exponent 3 and a Steiner triple system
.
We have:
satisfies the trapezium axiom
is self-distributive ⇔ (P, + ) is a Moufang loop
is an affine triple system; and:
satisfies the quadrangle axiom
is a group
is an affine space. 相似文献
4.
In this paper for a positive real number α we consider two partial differential operators D and Dα on the half–plane
We define a generalized Fourier transform
associated with the operators D and Dα. We establish an analogue of Beurling–H?rmander’s Theorem for this transform
and we give some applications of this theorem. 相似文献
5.
Jackson's Theorem on Bounded Symmetric Domains 总被引:1,自引:0,他引:1
Ming Zhi WANG Guang Bin REN 《数学学报(英文版)》2007,23(8):1391-1404
Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson's theorem to several complex variables:Eκ(f,X)≤ω(1/k,f,X), where Eκ(f,X) is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω(1/k,f,X) is the corresponding modulus of continuity. 相似文献
6.
It is known [6] that for every function f in the generalized Schur class
and every nonempty open subset Ω of the unit disk
, there exist points z1,...,zn ∈Ω such that the n × nPick matrix
has κ negative eigenvalues. In this paper we discuss existence of an integer n0 such that any Pick matrix based on z1,...,zn ∈Ω with n ≥ n0 has κ negative eigenvalues. Definitely, the answer depends on Ω. We prove that if
, then such a number n0 does not exist unless f is a ratio of two finite Blaschke products; in the latter case the minimal value of n0 can be found. We show also that if the closure of Ω is contained in
then such a number n0 exists for every function f in
. 相似文献
7.
The aim of this paper is to give the basic principles of hyperbolic function theory on the Clifford algebra . The structure of the theory is quite similar to the case of Clifford algebras with negative generators, but the proofs are
not obvious. The (real) Clifford algebra is generated by unit vectors with positive squares e2i = + 1. The hyperbolic Dirac operator is of the form where Q0f is represented by the composition . If is a solution of Hkf = 0, then f is called k-hypergenic in Ω, where is an open set. We introduce some basic results of hyperbolic function theory and give some representation theorems on .
Received: October, 2007. Accepted: February, 2008. 相似文献
8.
Trieu Le 《Integral Equations and Operator Theory》2009,63(4):547-555
For any α > −1, let A2α be the weighted Bergman space on the unit ball corresponding to the weight (1 – |z|2)α. We show that if all except possibly one of the Toeplitz operators are diagonal with respect to the standard orthonormal basis of A2α and has finite rank, then one of the functions must be the zero function.
相似文献
9.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
10.
Evgueni Doubtsov 《Integral Equations and Operator Theory》2009,64(2):177-192
Let Bn denote the unit ball of , n ≥ 2. Given an α > 0, let denote the class of functions defined for by integrating the kernel against a complex-valued measure on the sphere . Let denote the space of holomorphic functions in the ball. A function is called a multiplier of provided that for every . In the present paper, we obtain explicit analytic conditions on which imply that g is a multiplier of . Also, we discuss the sharpness of the results obtained.
This research was supported by RFBR (grant no. 08-01-00358-a), by the Russian Science Support Foundation and by the programme
“Key scientific schools NS 2409.2008.1”. 相似文献
11.
Yisheng Song 《Positivity》2009,13(4):643-655
In this paper, for a Lipschitz pseudocontractive mapping T, we study the strong convergence of iterative schemes generated by
, where f is a Lipschitz strong pseudocontractive mapping and {βn}, {αn} satisfy (i); (ii) ; (iii).
相似文献
12.
E. M. E. Zayed 《数学学报(英文版)》2000,16(4):627-636
Abstract
Small-time asymptotics of the trace of the heat semigroup
where {μ
ν
} are the eigenvalues of the negative Laplacian
in the (x
1, x
2)-plane, is studied for a general bunded domain Ω with a smooth boundary ∂Ω, where a finite number of Dirichlet, Neumann and
Robin boundary conditions, on the piecewise smooth parts Γ
i
(i = 1, ..., n) of ∂Ω such that
, are considered. Some geometrical properties associated with Ω are determined. 相似文献
13.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
14.
Let X1, X2,... be, i.i.d. random variables, and put
. We find necessary and sufficient moment conditions for
, where δ≥ 0 and q>0, and
with an>0 and bn is either
or
The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc 相似文献
15.
If
is an initially hereditary family of finite subsets of positive integers (i.e., if
and G is initial segment of F then
) and M an infinite subset of positive integers then we define an ordinal index
. We prove that if
is a family of finite subsets of positive integers such that for every
the characteristic function χF is isolated point of the subspace
of { 0,1 }N with the product topology then
for every
infinite, where
is the set of all initial segments of the members of
and ω1 is the first uncountable ordinal. As a consequence of this result we prove that
is Ramsey, i.e., if
is a partition of
then there exists an infinite subset M of positive integers such that
where [M]< ω is the family of all finite subsets of M. 相似文献
16.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
17.
Yong Ge TIAN 《数学学报(英文版)》2006,22(1):289-300
For any element a in a generalized 2^n-dimensional Clifford algebra Lln (F) over an arbitrary field F of characteristic not equal to two, it is shown that there exits a universal invertible matrix Pn over Lln(F) such that Pn^-1DnPn= φ(α)∈F^2n×2n, where φ(a) is a matrix representation of α over and Dα is a diagonal matrix consisting of a or its conjugate. 相似文献
18.
Self-dual 2–forms on
play a fundamental role in gauge theory. For generalized Seiberg-Witten theory (and for some other purposes in mathematical
physics) a notion of self-duality of 2–forms on
is needed. There are several definitions, but the one given by [Bilge, Dereli, Ko?ak ; JMP 38(9), 1997] is intimately related
with Clifford algebras. They defined a 2–form
to be self-dual if the anti-symmetric matrix Ω = (ωij) satisfies Ω2 = λ I for a scalar λ and proved that the space
of such forms is non-linear with dimension n2 − n + 1, but contains maximal linear subspaces with dimension the Radon-Hurwitz number of (2n). It is important to have an algorithm for construction of such maximal linear subspaces and we give an explicit one with
the help of representations of Clifford algebras on
whereby we show that the representations given by the standart recursion formulas are anti-symmetric. 相似文献
19.
Let E be a non empty set, let P : = E × E,
:= {x × E|x ∈ E},
:= {E × x|x ∈ E}, and
:= {C ∈ 2
P
|∀X ∈
: |C ∩ X| = 1} and let
. Then the quadruple
resp.
is called chain structure resp. maximal chain structure. We consider the maximal chain structure
as an envelope of the chain structure
. Particular chain structures are webs, 2-structures, (coordinatized) affine planes, hyperbola structures or Minkowski planes.
Here we study in detail the groups of automorphisms
,
,
,
related to a maximal chain structure
. The set
of all chains can be turned in a group
such that the subgroup
of
generated by
the left-, by
the right-translations and by ι the inverse map of
is isomorphic to
(cf. (2.14)). 相似文献
20.
E.M.E.ZAYED 《数学学报(英文版)》2003,19(4):679-694
The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. 相似文献