共查询到20条相似文献,搜索用时 62 毫秒
1.
Yu. V. Netrusov 《Journal of Mathematical Sciences》1989,47(6):2871-2881
The paper examines imbeddings of Besov spaces B
E, θ
ω
in ideal spaces (Banach lattices) given that ω ∈ Sk). In particular, the symmetric hull of the space B
E, θ
ω
is described (E is a symmetric space), an inequality of different metrics is obtained, and imbeddings in Orlicz and Lorentz
spaces and in some weighted spaces are studied. Most of the results are easily extended to the anisotropic case.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 159, pp. 69–82, 1987. 相似文献
2.
Veli B. SHAKHMUROV 《数学年刊B辑(英文版)》2008,29(1):95-112
This study focuses on the anisotropic Besov-Lions type spaces B^lp,θ(Ω;E0,E) associated with Banach spaces E0 and E. Under certain conditions, depending on l =(l1,l2,…,ln)and α=(α1,α2,…,αn),the most regular class of interpolation space Eα between E0 and E are found so that the mixed differential operators D^α are bounded and compact, from B^l+s p,θ(Ω;E0,E) to B^s p,θ(Ω;Eα).These results are applied to concrete vector-valued function spaces and to anisotropic differential-operator equations with parameters to obtain conditions that guarantee the uniform B separability with respect to these parameters. By these results the maximal B-regularity for parabolic Cauchy problem is obtained. These results are also applied to infinite systems of the quasi-elliptic partial differential equations and parabolic Cauchy problems with parameters to obtain sufficient conditions that ensure the same properties. 相似文献
3.
Jesús Bastero 《Israel Journal of Mathematics》1986,53(3):373-380
In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with
an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover,
we show that all the interpolation spacesl
p
,l
q
θ,X,1 1≦p, q<∞ andX stable, are stable. 相似文献
4.
Two inverse problems for the Sturm-Liouville operator Ly = s-y″ + q(x)y on the interval [0, fy] are studied. For θ ⩾ 0, there is a mapping F:W
2θ → l
B
θ, F(σ) = {s
k
}1∞, related to the first of these problems, where W
2∞ = W
2∞[0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q, and l
B
θ is a specially constructed finite-dimensional extension of the weighted space l
2θ, where we place the regularized spectral data s = {s
k
}1∞ in the problem of reconstruction from two spectra. The main result is uniform lower and upper bounds for ∥σ - σ1∥θ via the l
B
θ-norm ∥s − s1∥θ of the difference of regularized spectral data. A similar result is obtained for the second inverse problem, that is, the
problem of reconstructing the potential from the spectral function of the operator L generated by the Dirichlet boundary conditions. The result is new even for the classical case q ∈ L
2, which corresponds to θ = 1. 相似文献
5.
6.
U. Luther 《Annali di Matematica Pura ed Applicata》2003,182(2):161-200
We show that the representation theorem for classical approximation spaces can be generalized to spaces A(X,l
q
(ℬ))={f∈X:{E
n
(f)}∈l
q
(ℬ)} in which the weighted l
q
-space l
q
(ℬ) can be (more or less) arbitrary. We use this theorem to show that generalized approximation spaces can be viewed as real
interpolation spaces (defined with K-functionals or main-part K-functionals) between couples of quasi-normed spaces which satisfy certain Jackson and Bernstein-type inequalities. Especially,
interpolation between an approximation space and the underlying quasi-normed space leads again to an approximation space.
Together with a general reiteration theorem, which we also prove in the present paper, we obtain formulas for interpolation
of two generalized approximation spaces.
Received: December 6, 2001; in final form: April 2, 2002?Published online: March 14, 2003 相似文献
7.
This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal. 相似文献
8.
Avner Landver 《Israel Journal of Mathematics》1993,81(3):289-296
Letκ be a regular cardinal. Consider the Bair numbers of the spaces (2θ)κ for variousθ≥κ. Letl be the number of such different Baire numbers. Models of set theory withl=1 orl=2 are known and it is also known thatl is finite. We show here that ifκ>ω, thenl could be any given finite number. 相似文献
9.
Hans Triebel 《Annali di Matematica Pura ed Applicata》1977,113(1):33-42
Summary Let A be either B
p,
qs
or F
p,
qs
, where - ∞<s <∞; 0<p, q≦∞ (spaces of Besov-Hardy-Sobolev type, defined on Rn). (i) If g ∈C
ϱ (H?lder-Zygmund spaces), then f → gf is a bounded operator from A into A, provided that ϱ=ϱ(s, p, q, n) is large enough.
(ii) There are given sufficient conditions for s, p, and q ensuring that A is a subalgebra of C (space of uniformly continuous
bounded functions on Rn).
Entrata in Redazione il 17 marzo 1976. 相似文献
10.
M. F. Gamal' 《Journal of Mathematical Sciences》1997,85(2):1779-1789
A general scheme which enables us to consider convolution operators with measures acting in a wide class of spaces of distributions
on the interval [0, a), 0<a<∞, is represented. It is proved that if a measure μ is a weak generator of the algebra of measures
on [0, a), then Cμ (the convolution operator with μ) is unicellular. We give a condition for a measure μ under which the unicellularity of Cμ implies that μ is a weak generator of the algebra of measures. The following statement is also proved. Let
, Kθ=H2⊖θH2, and let Pθ be the orthogonal projector from H2 onto Kθ; in addition, let μ be a weak generator of the algebra of measures on [0, a) and
, z ∈
(here
is the unit disk and F-1 is the inverse Fourier transformation). Let ψ∈H∞ and let p be a polynomial such that p o(ψ−φ)∈θH∞. Then the operator x→Pθψx, acting in Kθ, is unicellular. Bibliography: 13 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 36–53. 相似文献
11.
Frank Aurzada 《Journal of Theoretical Probability》2007,20(4):843-858
We investigate the behaviour of the logarithmic small deviation probability of a sequence (σ
n
θ
n
) in l
p
, 0<p≤∞, where (θ
n
) are i.i.d. random variables and (σ
n
) is a decreasing sequence of positive numbers. In particular, the example σ
n
∼n
−μ
(1+log n)−ν
is studied thoroughly. Contrary to the existing results in the literature, the rate function and the small deviation constant
are expressed expli- citly in the present treatment. The restrictions on the distribution of θ
1 are kept to an absolute minimum. In particular, the usual variance assumption is removed. As an example, the results are
applied to stable and Gamma-distributed random variables. 相似文献
12.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
13.
For ν(dθ), a σ-finite Borel measure on R
d
, we consider L
2(ν(dθ))-valued stochastic processes Y(t) with te property that Y(t)=y(t,·) where y(t,θ)=∫
t
0
e
−λ(θ)(
t
−
s
)
dm(s,θ) and m(t,θ) is a continuous martingale with quadratic variation [m](t)=∫
t
0
g(s,θ)ds. We prove timewise H?lder continuity and maximal inequalities for Y and use these results to obtain Hilbert space regularity for a class of superrocesses as well as a class of stochastic evolutions
of the form dX=AXdt+GdW with W a cylindrical Brownian motion. Maximal inequalities and H?lder continuity results are also provenfor the path process
t
(τ)≗Y(τt∧t).
Received: 25 June 1999 / Revised version: 28 August 2000 /?Published online: 9 March 2001 相似文献
14.
V. V. Pukhnachov 《Journal of Mathematical Sciences》1997,84(1):911-918
Nonlocal transformations of some quasilinear parabolic equations which describe spherically symmetric heat conduction and
diffusion processes are considered. One of them transforms the equationr
n−1θ
t
=(r
n−1|θ
r
|
l
θ
r
)
r
to an equation of the same type but with a different value of the exponent n. Another transformation reduces the equationr
n−1θ
t
=(r
n−1θ−2θ
r
)
r
to an equation with coefficients which do not depend on the space variable. The third nonlocal transformation preserves the
equationrθ
t
=(rθ
−1θ
r
)
r
. Some exact solutions of the mentioned equations are analyzed. Bibliography: 15 titles.
Dedicated to V. A. Solonnikov on his sixtieth anniversary
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 151–163.
Translated by S. Yu. Pilyugin 相似文献
15.
Gabriella DiBlasio 《Semigroup Forum》1998,57(3):359-377
tA )t≥0 on X. We denote by XA(θ,p), for 0 < θ < 1, the interpolation spaces of X and D(A) introduced by Berens and Butzer in [1]. These spaces play an important
role in the approximation theory ( [2] ) as well as in the study of the abstract parabolic equation u′ (t) = Au(t) + f(t) ( [3] ). It has been proved in [6] that these spaces are meaningful (and still enjoy relevant properties) also in the case
θ = 0. In this paper we continue the study of [6] and prove new interesting properties of these spaces. 相似文献
16.
Bruno De Malafosse Eberhard Malkowsky 《Rendiconti del Circolo Matematico di Palermo》2002,51(2):277-294
We give here some properties of the sets
α(uΔ) generalizing the space of generalized difference sequencesl
∞(uΔ). Then we study spaces related to the sets of sequences that are strongly convergent or strongly bounded. Next we define
from the sets of spaces that are (N,q) summable or bounded the sets of spaces that are (N,q)α-bounded orr-bounded. Then we give some properties of these spaces using Banach space of the forms
α. 相似文献
17.
We prove that the Banach space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{\ell_{q}}, which is isomorphic to certain Besov spaces, has a greedy basis whenever 1≤p≤∞ and 1<q<∞. Furthermore, the Banach spaces (?n=1¥lpn)l1(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{1}}, with 1<p≤∞, and (?n=1¥lpn)c0(\bigoplus_{n=1}^{\infty}\ell_{p}^{n})_{c_{0}}, with 1≤p<∞, do not have a greedy basis. We prove as well that the space (?n=1¥lpn)lq(\bigoplus_{n=1}^{\infty}\ell _{p}^{n})_{\ell_{q}} has a 1-greedy basis if and only if 1≤p=q≤∞. 相似文献
18.
Summary We prove a Schur test for mixed-norm spaces Lp,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces lp,q w, 1 < p,q < ∞, and wis a weight. We show that if w 1, and w 2are two weight functions on the index sets Jx Iand K x Lrespectively, and A =(a ji, kl ) j∈J, i∈I, k∈K, l∈L is an infinite matrix, then under certain conditions, Ais a bounded operator from lp,q w1, 1 < p,q < ∞ to lp,q w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.</o:p> 相似文献
19.
Abstract
Let μ and ν be normal functions and let T
g
be the extended Cesàso operator in terms of the symbol g. In this paper, we will characterize those g so that T
g
is bounded (or compact) from mixed norm spaces H(p, q, μ) to H(p, q, ν) in the unit ball of C
n
. Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces.
Supported by the National Natural Science Foundation of China (No.10571049, 10471039), the Natural Science Foundation of Zhejiang
Province (No. M103085). 相似文献
20.
Paul F. X. Müller 《Israel Journal of Mathematics》1987,59(2):195-212
LetF
n be an increasing sequence of finite fields on a probability space (Ω,F
n,P) whereF denotes the σ-algebra generated by ∪F
n. ThenF
n is isomorphic to one of the following spaces:H
1(δ), ΣH
n
1
,l
l. 相似文献