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1.
In this paper, we obtain inequalities for maximal functions of fractional differences and fractional derivatives and use them to prove that in the Lizorkin--Triebel spaces Fs
pq=Fs
pq(n), 0 < p < , 0 q , given sufficient smoothness s > 0, we can introduce equivalent quasinorms expressible in terms of fractional differences of order > s. 相似文献
2.
Multipliers and Cyclic Vectors in Bloch Type Spaces 总被引:6,自引:0,他引:6
In this paper we study the coefficient multipliers, pointwise multipliers and cyclic vectors in the Bloch type spaces B
α
and little Bloch type spaces
for 0 < α < ∞. We give several full characterizations of the coefficient multipliers (B
α
,B
β
) and
for 0 < α, β < ∞ and pointwise multipliers M(B
α
,B
β
) and
for 1 ≠ α, β ∈ (0,∞). We also obtain some properties of cyclic vectors for Bloch type spaces.
Dedicated to Professor Yu Zan HE on the occasion of his 65th birthday 相似文献
3.
Jan Schneider 《Mathematische Nachrichten》2007,280(16):1801-1826
This paper deals with function spaces of varying smoothness. It is a modified version of corresponding parts of [8]. Corresponding spaces of positive smoothness s (x) will be considered in part II. We define the spaces Bp (?n ), where the function ??: x ? s (x) is negative and determines the smoothness pointwise. First we prove basic properties and then we use different wavelet decompositions to get information about the local smoothness behavior. The main results are characterizations of the spaces Bp (?n ) by weighted sequence space norms of the wavelet coefficients. These assertions are used to prove an interesting connection to the so‐called two‐microlocal spaces Cs,s ′ (x0). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
Let E be a symmetric space on [0,1]. Let (,E) be the space of measurable functions f such that fg E for every almost everywhere convergent series g=b
n
r
n E, where (r
n) are the Rademacher functions. It was shown that, for a broad class of spaces E, the space (,E) is not order isomorphic to a symmetric space, and we study the conditions under which such an isomorphism exists. We give conditions on E for (,E) to be order isomorphic to L
. This includes some classes of Lorentz and Marcinkiewicz spaces. We also study the conditions under which (,E) is order isomorphic to a symmetric space that differs from L
. The answer is positive for the Orlicz spaces E=L
q with q(t)=exp|t|q-1 and 0
相似文献
5.
In the literature (see [5, 6, 8]) there are two families of spaces called Kondratiev spaces: (c)± and (S
c)± for 0 1. We investigate the relation between the spaces and show that they are topologically isomorphic when (d) L2 (d) (d) is the underlying Gel'fand triple for (c)±. In this case we also give the explicit relation between the S-transform and -transform on (c)-1 and (S
c)-1, respectively. 相似文献
6.
Berthold Wittje 《Journal of Theoretical Probability》2000,13(1):85-92
It is well known, that for the sums of i.i.d. random variables we have S
n/n 0 a.s. iff
n=1 1/n
P(|S
n| > n) < holds for all > 0 (Spitzer's SLLN). The result is also known in separable Banach spaces. It will be shown, that this also holds in nonseparable (= not necessarily separable) Banach spaces without any measurability assumption. In the theory of empirical processes this gives a characterization of Glivenko-Cantelli classes. 相似文献
7.
This paper generalizes the mixed extension principle in L
2(ℝ
d
) of (Ron and Shen in J. Fourier Anal. Appl. 3:617–637, 1997) to a pair of dual Sobolev spaces H
s
(ℝ
d
) and H
−s
(ℝ
d
). In terms of masks for φ,ψ
1,…,ψ
L
∈H
s
(ℝ
d
) and
, simple sufficient conditions are given to ensure that (X
s
(φ;ψ
1,…,ψ
L
),
forms a pair of dual wavelet frames in (H
s
(ℝ
d
),H
−s
(ℝ
d
)), where
For s>0, the key of this general mixed extension principle is the regularity of φ, ψ
1,…,ψ
L
, and the vanishing moments of
, while allowing
,
to be tempered distributions not in L
2(ℝ
d
) and ψ
1,…,ψ
L
to have no vanishing moments. So, the systems X
s
(φ;ψ
1,…,ψ
L
) and
may not be able to be normalized into a frame of L
2(ℝ
d
). As an example, we show that {2
j(1/2−s)
B
m
(2
j
⋅−k):j∈ℕ0,k∈ℤ} is a wavelet frame in H
s
(ℝ) for any 0<s<m−1/2, where B
m
is the B-spline of order m. This simple construction is also applied to multivariate box splines to obtain wavelet frames with short supports, noting
that it is hard to construct nonseparable multivariate wavelet frames with small supports. Applying this general mixed extension
principle, we obtain and characterize dual Riesz bases
in Sobolev spaces (H
s
(ℝ
d
),H
−s
(ℝ
d
)). For example, all interpolatory wavelet systems in (Donoho, Interpolating wavelet transform. Preprint, 1997) generated by an interpolatory refinable function φ∈H
s
(ℝ) with s>1/2 are Riesz bases of the Sobolev space H
s
(ℝ). This general mixed extension principle also naturally leads to a characterization of the Sobolev norm of a function in
terms of weighted norm of its wavelet coefficient sequence (decomposition sequence) without requiring that dual wavelet frames
should be in L
2(ℝ
d
), which is quite different from other approaches in the literature.
相似文献
8.
In this paper we prove that the moduli spaces MI
2n+1(k) of mathematical instanton bundles on 2n+1
with quantum number k are singular for n 2 and k 3 ,giving a positive answer to a conjecture made by Ancona and Ottaviani in 1993. 相似文献
9.
Jacek Dziubański 《Journal of Fourier Analysis and Applications》2009,15(2):129-152
Let L
n
a
(x), n=0,1,…, be the Laguerre polynomials of order a>−1. Denote ℓ
n
a
(x)=(n!/Γ(n+a+1))1/2
L
n
a
(x)e
−x/2. Let
be the kernel of the semigroup {T
t
}
t>0 associated with the system ℓ
n
a
considered on ((0,∞),x
a
dx). We say that a function f belongs to the Hardy space H
1 associated with the semigroup if the maximal function
belongs to L
1((0,∞),x
a
dx). We prove a special atomic decomposition of the elements of the Hardy space.
Research supported by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic Analysis,
Nonlinear Analysis and Probability” MTKD-CT-2004-013389, and by Polish funds for science in the years 2005–2008 (research
project 1P03A03029). 相似文献
10.
For a class of closed sets F R
n
admitting a regular sequence of triangulations or generalized triangulations, the analogues on F of the Faber—Schauder and Franklin bases are discussed. The characterizations of the Besov spaces on F in the terms of coefficients of functions with respect to these bases are proved. As a consequence, analogous characterizations of the Besov spaces on some fractal domains (including the Sierpinski gasket and the von Koch curve) by coefficients of functions with respect to the wavelet bases constructed in [26] are obtained. 相似文献
11.
Some Groups Having Only Elementary Actions on Metric Spaces with Hyperbolic Boundaries 总被引:1,自引:0,他引:1
We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SL
n
(), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(-1) and Gromov hyperbolic spaces. We also show that SL
n
() for n 3 cannot act on a visibility space X without fixing a point in
. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included. 相似文献
12.
Let (E
i
)
iI
be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E
i
)
iI
of spaces is
Starting from the topology on and the norm topology on each E
i
, a natural topology on {(E
i
)
iI
} can be defined. We give conditions for {(E
i
)
iI
} to be quasi-barrelled, barrelled or locally complete. 相似文献
13.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
14.
We determine which information can be extracted from the distributions of the
wavelet coefficients of a function f at each scale, but does not depend on the particular wavelet basis
which is chosen. This information can be naturally expressed in terms of one increasing function
f (), and the knowledge of this function yields strictly more information than the knowledge of
the Besov spaces that contain f . Examples of use of this additional information will be taken from
image processing and multifractal analysis. 相似文献
15.
Sobolev type spaces E
s,p
(0, sR, p[1,+]) are defined on R×N by using the Fourier transform and its inverse on the Laguerre hypergroup. An analogue of H
s
(R
n
), denoted by H
s
is investigated in this paper. Some properties including completeness and imbedding results for these spaces are given, Reillich-type theorem and Poincaré's inequality are proved. Also, global regularity results for certain differential operators are obtained. 相似文献
16.
P. Bieliavsky 《Geometriae Dedicata》1998,73(3):245-273
A symplectic symmetric space is a connected affine symmetric manifold M endowed with a symplectic structure which is invariant under the geodesic symmetries. When the transvection group G0 of such a symmetric space M is semisimple, its action on (M,) is strongly Hamiltonian; a classical theorem due to Kostant implies that the moment map associated to this action realises a G0-equivariant symplectic covering of a coadjoint orbit O in the dual of the Lie algebra
of G0. We show that this orbit itself admits a structure of symplectic symmetric space whose transvection algebra is
. The main result of this paper is the classification of symmetric orbits for any semisimple Lie group. The classification is given in terms of root systems of transvection algebras and therefore provides, in a symplectic framework, a theorem analogous to the Borel–de Siebenthal theorem for Riemannian symmetric spaces. When its dimension is greater than 2, such a symmetric orbit is not regular and, in general, neither Hermitian nor pseudo-Hermitian. 相似文献
17.
Singular Integrals and Commutators in Generalized Morrey Spaces 总被引:1,自引:0,他引:1
Lubomiea Softova 《数学学报(英文版)》2006,22(3):757-766
18.
Haiou Tan 《Analysis Mathematica》2000,26(2):119-132
Let be a normal function on [0, 1), B
n
the unit ball of C
n
, and A
p
(B
n
) the weighted Bergman spaces on B
n
with weight . The purpose of this paper is to discuss some relations among A
p
(B
n
), weighted Bergman kernels, and Carleson measures on B
n
. 相似文献
19.
We review the proposal of a constructive axiomatic approach to the determination of the orbit spaces of all the real compact linear groups, obtained through the computation of a metric matrix
, which is defined only in terms of the scalar products between the gradients p1(x),...,pq(x) of the elements of a minimal integrity basis (MIB) for the ring [n]G of G-invariant polynomials. The domain of semi-positivity of
is known to realize the orbit space n/G of G as a semi-algebraic variety in the space q spanned by the variables p1,...,pq.
The matrices
can be obtained from the solutions of a universal differential equation (master equation), which satisfy convenient initial conditions. The master equation and the initial conditions involve as free parameters only the degrees da of the pa(x)s. This approach tries to bypass the actual impossibility of explicitly determining a set of basic polynomial invariants for each group.
Our results may be relevant in physical contexts where the study of covariant or invariant functions is important, like in the determination of patterns of spontaneous symmetry breaking in quantum field theory, in the analysis of phase spaces and structural phase transitions (Landaus theory), in covariant bifurcation theory, in crystal field theory and so on.
Mathematics Subject Classifications (2000) 14L24, 13A50, 14L30.This paper is partially supported by INFN and MURST 40% and 60%. 相似文献
20.
Thomas Schott 《Mathematische Nachrichten》1998,196(1):231-250
This paper is a continuation of [8]. We study weighted function spaces of type B and F on the Euclidean space Rn, where u is a weight function of at most exponential growth. In particular, u(χ (±|χ|) is an admissible weight. We deal with atomic decompositions of these spaces. Furthermore, we prove that the spaces B and F are isomorphic to the corresponding unweighted spaces B and F. 相似文献