共查询到20条相似文献,搜索用时 125 毫秒
1.
Violeta Petkova 《Archiv der Mathematik》2009,93(4):357-368
We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces ${L_{\omega}^{2}(\mathbb{R})}We study the spectrum σ(M) of the multipliers M which commute with the translations on weighted spaces
Lw2(\mathbbR){L_{\omega}^{2}(\mathbb{R})} For operators M in the algebra generated by the convolutions with
f ? Cc(\mathbb R){\phi \in {C_c(\mathbb {R})}} we show that [`(m(W))] = s(M){\overline{\mu(\Omega)} = \sigma(M)}, where the set Ω is determined by the spectrum of the shift S and μ is the symbol of M. For the general multipliers M we establish that [`(m(W))]{\overline{\mu(\Omega)}} is included in σ(M). A generalization of these results is given for the weighted spaces
L2w(\mathbb Rk){L^2_{\omega}(\mathbb {R}^{k})} where the weight ω has a special form. 相似文献
2.
Let ${s,\,\tau\in\mathbb{R}}Let
s, t ? \mathbbR{s,\,\tau\in\mathbb{R}} and q ? (0,¥]{q\in(0,\infty]} . We introduce Besov-type spaces
[(B)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} for p ? (0, ¥]{p\in(0,\,\infty]} and Triebel–Lizorkin-type spaces
[(F)\dot]s, tp, q(\mathbbRn) for p ? (0, ¥){{{{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}\,{\rm for}\, p\in(0,\,\infty)} , which unify and generalize the Besov spaces, Triebel–Lizorkin spaces and Q spaces. We then establish the j{\varphi} -transform characterization of these new spaces in the sense of Frazier and Jawerth. Using the j{\varphi} -transform characterization of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\, {\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} , we obtain their embedding and lifting properties; moreover, for appropriate τ, we also establish the smooth atomic and
molecular decomposition characterizations of
[(B)\dot]s, tp, q(\mathbbRn) and [(F)\dot]s, tp, q(\mathbbRn){{{{\dot B}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}\,{\rm and}\, {{\dot F}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}} . For
s ? \mathbbR{s\in\mathbb{R}} , p ? (1, ¥), q ? [1, ¥){p\in(1,\,\infty), q\in[1,\,\infty)} and
t ? [0, \frac1(max{p, q})¢]{\tau\in[0,\,\frac{1}{(\max\{p,\,q\})'}]} , via the Hausdorff capacity, we introduce certain Hardy–Hausdorff spaces
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} and prove that the dual space of
B[(H)\dot]s, tp, q(\mathbbRn){{{{B\dot{H}^{s,\,\tau}_{p,\,q}(\mathbb{R}^{n})}}}} is just
[(B)\dot]-s, tp¢, q¢(\mathbbRn){\dot{B}^{-s,\,\tau}_{p',\,q'}(\mathbb{R}^{n})} , where t′ denotes the conjugate index of t ? (1,¥){t\in (1,\infty)} . 相似文献
3.
Susana D. Moura J��lio S. Neves Cornelia Schneider 《Journal of Fourier Analysis and Applications》2011,17(5):777-800
We study necessary and sufficient conditions for embeddings of Besov and Triebel-Lizorkin spaces of generalized smoothness
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), respectively, into generalized H?lder spaces
L¥,rm(·)( \mathbb Rn)\Lambda_{\infty,r}^{\mu(\cdot)}(\ensuremath {\ensuremath {\mathbb {R}}^{n}}). In particular, we are able to characterize optimal embeddings for this class of spaces provided q>1. These results improve the embedding assertions given by the continuity envelopes of
B(n/p,Y)p,q(\mathbbRn)B^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}) and
F(n/p,Y)p,q(\mathbbRn)F^{(n/p,\Psi)}_{p,q}(\mathbb{R}^{n}), which were obtained recently solving an open problem of D.D. Haroske in the classical setting. 相似文献
4.
Ronggang Shi 《Monatshefte für Mathematik》2012,165(3-4):513-541
We consider improvements of Dirichlet’s Theorem on the space of matrices ${M_{m,n}(\mathbb R)}$ . It is shown that for a certain class of fractals ${K\subset [0,1]^{mn}\subset M_{m,n}(\mathbb R)}$ of local maximal dimension Dirichlet’s Theorem cannot be improved almost everywhere. This is shown using entropy and dynamics on homogeneous spaces of Lie groups. 相似文献
5.
Milo? S. Kurili? 《Order》2012,29(1):119-129
A family P ì [w]w{\mathcal P} \subset [\omega]^\omega is called positive iff it is the union of some infinite upper set in the Boolean algebra P(ω)/Fin. For example, if I ì P(w){\mathcal I} \subset P(\omega) is an ideal containing the ideal Fin of finite subsets of ω, then P(w) \IP(\omega) \setminus {\mathcal I} is a positive family and the set
Dense(\mathbb Q)\mbox{Dense}({\mathbb Q}) of dense subsets of the rational line is a positive family which is not the complement of some ideal on
P(\mathbb Q)P({\mathbb Q}). We prove that, for a positive family P{\mathcal P}, the order types of maximal chains in the complete lattice áP è{?}, ì ?\langle {\mathcal P} \cup \{\emptyset\}, \subset \rangle are exactly the order types of compact nowhere dense subsets of the real line having the minimum non-isolated. Also we compare
this result with the corresponding results concerning maximal chains in the Boolean algebras P(ω) and
Intalg[0,1)\mathbb R\mbox{Intalg}[0,1)_{{\mathbb R}} and the poset
E(\mathbb Q)E({\mathbb Q}), where
E(\mathbb Q)E({\mathbb Q}) is the set of elementary submodels of the rational line. 相似文献
6.
Jörg Eschmeier 《Integral Equations and Operator Theory》2011,69(2):171-182
Let
M ì H(\mathbbB){M \subset H(\mathbb{B})} be a homogeneous submodule of the n-shift Hilbert module on the unit ball in
\mathbbCn{\mathbb{C}^{n}}. We show that a modification of an operator inequality used by Guo and Wang in the case of principal submodules is equivalent
to the existence of factorizations of the form [Mzj*,PM] = (N+1)-1Aj{[M_{z_j}^*,P_M] = (N+1)^{-1}A_j}, where N is the number operator on
H(\mathbbB){H(\mathbb{B})}. Thus a proof of the inequality would yield positive answers to conjectures of Arveson and Douglas concerning the essential
normality of homogeneous submodules of
H(\mathbbB){H(\mathbb{B})}. We show that in all cases in which the conjectures have been established the inequality holds and leads to a unified proof
of stronger results. 相似文献
7.
Matteo Dalla Riva Massimo Lanza de Cristoforis 《Complex Analysis and Operator Theory》2011,5(3):811-833
Let Ω
i
and Ω
o
be two bounded open subsets of
\mathbbRn{{\mathbb{R}}^{n}} containing 0. Let G
i
be a (nonlinear) map from
?Wi×\mathbbRn{\partial\Omega^{i}\times {\mathbb{R}}^{n}} to
\mathbbRn{{\mathbb{R}}^{n}} . Let a
o
be a map from ∂Ω
o
to the set
Mn(\mathbbR){M_{n}({\mathbb{R}})} of n × n matrices with real entries. Let g be a function from ∂Ω
o
to
\mathbbRn{{\mathbb{R}}^{n}} . Let γ be a positive valued function defined on a right neighborhood of 0 in the real line. Let T be a map from
]1-(2/n),+¥[×Mn(\mathbbR){]1-(2/n),+\infty[\times M_{n}({\mathbb{R}})} to
Mn(\mathbbR){M_{n}({\mathbb{R}})} . Then we consider the problem
$\left\{ {ll} {{\rm div}}\, (T(\omega,Du))=0 &\quad {{\rm in}} \;\Omega^{o} \setminus\epsilon{{\rm cl}} \Omega^{i},\\ -T(\omega,Du(x))\nu_{\epsilon\Omega^{i}}(x)=\frac{1}{\gamma(\epsilon)}G^{i}({x}/{\epsilon}, \gamma(\epsilon)\epsilon^{-1} ({\rm log} \, \epsilon)^{-\delta_{2,n}} u(x)) & \quad \forall x \in \epsilon\partial\Omega^{i},\\ T(\omega, Du(x)) \nu^{o}(x)=a^{o}(x)u(x)+g(x) & \quad \forall x \in \partial \Omega^{o}, \right.$\left\{ \begin{array}{ll} {{\rm div}}\, (T(\omega,Du))=0 &\quad {{\rm in}} \;\Omega^{o} \setminus\epsilon{{\rm cl}} \Omega^{i},\\ -T(\omega,Du(x))\nu_{\epsilon\Omega^{i}}(x)=\frac{1}{\gamma(\epsilon)}G^{i}({x}/{\epsilon}, \gamma(\epsilon)\epsilon^{-1} ({\rm log} \, \epsilon)^{-\delta_{2,n}} u(x)) & \quad \forall x \in \epsilon\partial\Omega^{i},\\ T(\omega, Du(x)) \nu^{o}(x)=a^{o}(x)u(x)+g(x) & \quad \forall x \in \partial \Omega^{o}, \end{array} \right. 相似文献
8.
Let L be a divergence form elliptic operator with complex bounded measurable coefficients, ω a positive concave function on (0, ∞) of strictly critical lower type p ω ∈(0, 1] and ρ(t) = t ?1/ω ?1(t ?1) for ${t\in (0,\infty).}
9.
In this note we give a simple method to transfer the effect of the surface to the radial function in the kernel of singular
integral along surface. Using this idea, we give some continuity of the singular integrals along surface with Hardy space
function kernels on some function spaces, such as
Lp(\mathbb Rn),Lp(\mathbb Rn,w){L^p({\mathbb R}^n),L^p({\mathbb R}^n,\omega)}, Triebel–Lizorkin spaces
[(F)\dot]ps,q(\mathbb Rn){{\dot F}_{p}^{s,q}({\mathbb R}^n)}, Besov spaces
[(B)\dot]ps,q(\mathbb Rn){{\dot B}_{p}^{s,q}({\mathbb R}^n)}, generalized Morrey spaces
Lp,f(\mathbb Rn){L^{p,\phi}({\mathbb R}^n)} and Herz spaces
[(K)\dot]pa, q(\mathbb Rn){\dot K_p^{\alpha, q}({\mathbb R}^n)}. Our results improve and extend substantially some known results on the singular integral operators along surface. 相似文献
10.
Françoise Lust-Piquard 《Potential Analysis》2006,24(1):47-62
Let L=?Δ+|ξ|2 be the harmonic oscillator on $\mathbb{R}^{n}
|