共查询到20条相似文献,搜索用时 32 毫秒
1.
Fayou Zhao 《Mathematische Nachrichten》2012,285(10):1294-1298
Fu and Lu et al. 7 showed that the commutator $\mathcal {H}_{\beta ,b}$ generated by the fractional Hardy operator and a locally integrable function b is bounded on the homogenous Herz spaces if and only if b is a central bounded mean oscillation function. We show that their result is optimal by giving a counterexample. 相似文献
2.
3.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2012,58(3):130-138
Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:
- (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
- (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
- (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
- (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.
4.
In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type $\dot{F}^{\alpha,q}_{b,p}In this article, we use a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a
para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type
, which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a
necessary and sufficient condition for the
boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with M
b
TM
b
∈WBP is bounded from
to
if and only if
and T
*
b=0 for
, where ε is the regularity exponent of the kernel of T.
Chin-Cheng Lin supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-008-021-MY3.
Kunchuan Wang supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-259-009 and NCU Center for
Mathematics and Theoretic Physics. 相似文献
5.
Zak Mesyan James D. Mitchell Michał Morayne Yann H. Péresse 《Mathematical Logic Quarterly》2012,58(6):424-433
Let $\mathbb {N}^\mathbb {N}Let $\mathbb {N}^\mathbb {N}$ be the semigroup of all mappings on the natural numbers $\mathbb {N}$, and let U and V be subsets of $\mathbb {N}^\mathbb {N}$. We write U?V if there exists a countable subset C of $\mathbb {N}^\mathbb {N}$ such that U is contained in the subsemigroup generated by V and C. We give several results about the structure of the preorder ?. In particular, we show that a certain statement about this preorder is equivalent to the Continuum Hypothesis. The preorder ? is analogous to one introduced by Bergman and Shelah on subgroups of the symmetric group on $\mathbb {N}$. The results in this paper suggest that the preorder on subsemigroups of $\mathbb {N}^\mathbb {N}$ is much more complicated than that on subgroups of the symmetric group. 相似文献
6.
Jacob Mostovoy 《Transactions of the American Mathematical Society》2001,353(5):1959-1970
We show that the loop spaces on real projective spaces are topologically approximated by the spaces of rational maps . As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic (degree) of an ornament via particle spaces.
7.
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In this paper, we will give some optimal estimates on the rotation number of the linear equation
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x = 0,
and that of the asymmetric equation:
$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,$\ifmmode\expandafter\ddot\else\expandafter\"\fi{x} + p(t)x_{ + } + q(t)x_{ - } = 0,
where p(t) and q(t) are almost periodic functions and
x + = max{ x,0} , x - = min{ x,0} .x_{ + } = \max \{ x,0\} ,\;x_{ - } = \min \{ x,0\} .
These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions. 相似文献
9.
Roland Sh. Omanadze 《Mathematical Logic Quarterly》2013,59(3):238-246
We study the degree structure of bQ‐reducibility and we prove that for any noncomputable c.e. incomplete bQ‐degree a, there exists a nonspeedable bQ‐degree incomparable with it. The structure $\mathcal {D}_{\mbox{bs}}$ of the $\mbox{bs}$‐degrees is not elementary equivalent neither to the structure of the $\mbox{be}$‐degrees nor to the structure of the $\mbox{e}$‐degrees. If c.e. degrees a and b form a minimal pair in the c.e. bQ‐degrees, then a and b form a minimal pair in the bQ‐degrees. Also, for every simple set S there is a noncomputable nonspeedable set A which is bQ‐incomparable with S and bQ‐degrees of S and A does not form a minimal pair. 相似文献
10.
T. Mitsis 《Archiv der Mathematik》2003,81(2):229-232
We prove that if F is a subset of the
2-dimensional unit sphere in $\mathbb{R}^3$, with Hausdorff dimension
strictly greater than 1, and E is a subset of
$\mathbb{R}^3$ such that for each $e \in F$, E contains a plane perpendicular
to the vector e, then
E must have positive 3-dimensional
Lebesgue measure.Received: 16 April 2002 相似文献
11.
We prove several dichotomy theorems which extend some known results on σ‐bounded and σ‐compact pointsets. In particular we show that, given a finite number of $\Delta ^{1}_{1}$ equivalence relations $\mathrel {\mathsf {F}}_1,\dots ,\mathrel {\mathsf {F}}_n$, any $\Sigma ^{1}_{1}$ set A of the Baire space either is covered by compact $\Delta ^{1}_{1}$ sets and lightface $\Delta ^{1}_{1}$ equivalence classes of the relations $\mathrel {\mathsf {F}}_i$, or A contains a superperfect subset which is pairwise $\mathrel {\mathsf {F}}_i$‐inequivalent for all i = 1, …, n. Further generalizations to $\Sigma ^{1}_{2}$ sets A are obtained. 相似文献
12.
We establish the following Helly-type theorem: Let ${\cal K}$ be a family of
compact sets in $\mathbb{R}^d$. If every d + 1 (not necessarily
distinct) members of ${\cal K}$ intersect in a starshaped set whose kernel
contains a translate of set A, then
$\cap \{ K : K\; \hbox{in}\; {\cal K} \}$ also is a starshaped set whose kernel contains a
translate of A. An analogous result holds
when ${\cal K}$ is a finite family of closed sets in $\mathbb{R}^d$.
Moreover, we have the following planar result: Define function f on
$\{0, 1, 2\}$ by f(0) = f(2) = 3, f(1) = 4. Let ${\cal K}$ be a finite
family of closed sets in the plane. For k = 0, 1, 2, if every f(k)
(not necessarily distinct) members of ${\cal K}$ intersect in a starshaped set
whose kernel has dimension at least k,
then $\cap \{K : K\; \hbox{in}\; {\cal K}\}$ also is a starshaped set whose kernel has
dimension at least k. The number f(k) is best
in each case.Received: 4 June 2002 相似文献
13.
We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces Aq(logA)b,q A_{\theta}({\log}A)_{b,q} and in the Zygmund spaces Lp(logL)b(W) L_p({\log}L)_b(\Omega) , for
b ? \mathbbR b \in \mathbb{R} and for suitable 1 £ p £ 2 1 \leq p \leq 2 . As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces. 相似文献
14.
15.
For integers
, we consider
-valued Radon measures
on an open set
which satisfy
for all
. We show that under certain conditions,
]*> has an (n - p)-dimensional density everywhere, and the set of points of positive density is countably (n - p)-rectifiable. This simplifies the proofs of several rectifiability theorems involving varifolds with vanishing first variations, p-harmonic maps, or Yang-Mills connections.Received: 4 April 2002, Accepted: 16 June 2002, Published online: 5 September 2002Mathematics Subject Classification (1991):
49Q15, 49Q05, 58E20, 58E15 相似文献
16.
Given a local quantum field theory net $ \mathcal{A} $ on the de Sitter spacetime dS
d
,
where geodesic observers are thermalized at Gibbons-Hawking temperature, we look
for observers that feel to be in a ground state, i.e., particle evolutions with positive
generator, providing a sort of converse to the Hawking-Unruh effect. Such positive
energy evolutions always exist as noncommutative flows, but have only a partial
geometric meaning, yet they map localized observables into localized observables.
We characterize the local conformal nets on dS
d
. Only in this case our positive
energy evolutions have a complete geometrical meaning. We show that each net
has a unique maximal expected conformal subnet, where our evolutions are thus
geometrical.
In the two-dimensional case, we construct a holographic one-to-one correspondence
between local nets $ \mathcal{A} $ on dS
2 and local conformal non-isotonic families
(pseudonets) $ \mathcal{B} $ on S
1. The pseudonet $ \mathcal{B} $ gives rise to two local conformal nets
$ \mathcal{B}_\pm $ on S
1, that correspond to the $ \frak{H}_\pm $ horizon components of $ \mathcal{A} $, and to the chiral
components of the maximal conformal subnet of $ \mathcal{A} $. In particular, $ \mathcal{A} $ is holographically
reconstructed by a single horizon component, namely the pseudonet is a net,
iff the translations on $ \frak{H}_\pm $ have positive energy and the translations on $ \frak{H}_\mp $ are
trivial. This is the case iff the one-parameter unitary group implementing rotations
on dS
2 has positive/negative generator.
Communicated by Klaus Fredenhagen
submitted 07/02/03, accepted: 07/07/03 相似文献
17.
本文的主要建立非齐性度量测度空间上双线性强奇异积分算子$\widetilde{T}$及交换子$\widetilde{T}_{b_{1},b_{2}}$在广义Morrey空间$M^{u}_{p}(\mu)$上的有界性. 在假设Lebesgue可测函数$u, u_{1}, u_{2}\in\mathbb{W}_{\tau}$, $u_{1}u_{2}=u$,且$\tau\in(0,2)$. 证明了算子$\widetilde{T}$是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到空间$M^{u}_{p}(\mu)$有界的, 也是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到广义弱Morrey空间$WM^{u}_{p}(\mu)$有界的,其中$\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$及$1相似文献
18.
19.
It is shown that for every quasi-normed ideal ${\cal Q}$ of
n-homogeneous continuous polynomials between
Banach spaces there is a quasi-normed ideal ${\cal A}$ of
n-linear continuous mappings ${\cal A}$ such that
$q \in {\cal Q}$ if and only if the associated n-linear
mapping $\check{q}$ of q is in ${\cal A}$.
Received: 12 March 2001 相似文献
20.
Assume that we want to recover $f : \Omega \to {\bf C}$ in the
$L_r$-quasi-norm ($0 < r \le \infty$) by a linear sampling method
$$
S_n f = \sum_{j=1}^n f(x^j) h_j ,
$$
where $h_j \in L_r(\Omega )$ and $x^j \in \Omega$
and $\Omega \subset {\bf R}^d$ is an arbitrary bounded Lipschitz domain.
We assume that $f$ is from the unit ball of
a Besov space $B^s_{pq} (\Omega)$ or of a
Triebel--Lizorkin space $F^s_{pq} (\Omega)$ with
parameters such that the space is compactly embedded
into $C(\overline{\Omega})$. We prove that the optimal rate
of convergence of linear sampling methods is
$$
n^{ -{s}/{d} + ({1}/{p}-{1}/{r})_+} ,
$$
nonlinear methods do not yield a better rate.
To prove this we use a result from Wendland (2001) as well
as results concerning the spaces $B^s_{pq} (\Omega) $ and $F^s_{pq}(\Omega)$.
Actually, it is another aim of this paper to complement the
existing literature about the function spaces $B^s_{pq} (\Omega)$ and $F^s_{pq}
(\Omega)$ for bounded Lipschitz domains $\Omega \subset {\bf R}^d$.
In this sense, the paper is also a continuation of a paper by Triebel (2002). 相似文献