共查询到20条相似文献,搜索用时 46 毫秒
1.
Masato Kikuchi 《Mathematische Zeitschrift》2010,265(4):865-887
Let ${\Phi : \mathbb{R} \to [0, \infty)}Let
F: \mathbbR ? [0, ¥){\Phi : \mathbb{R} \to [0, \infty)} be a Young function and let
f = (fn)n ? \mathbbZ+{f = (f_n)_n\in\mathbb{Z}_{+}} be a martingale such that F(fn) ? L1{\Phi(f_n) \in L_1} for all
n ? \mathbbZ+{n \in \mathbb{Z}_{+}} . Then the process
F(f) = (F(fn))n ? \mathbbZ+{\Phi(f) = (\Phi(f_n))_n\in\mathbb{Z}_{+}} can be uniquely decomposed as F(fn)=gn+hn{\Phi(f_n)=g_n+h_n} , where
g=(gn)n ? \mathbbZ+{g=(g_n)_n\in\mathbb{Z}_{+}} is a martingale and
h=(hn)n ? \mathbbZ+{h=(h_n)_n\in\mathbb{Z}_{+}} is a predictable nondecreasing process such that h
0 = 0 almost surely. The main results characterize those Banach function spaces X such that the inequality ||h¥||X £ C ||F(Mf) ||X{\|{h_{\infty}}\|_{X} \leq C \|{\Phi(Mf)} \|_X} is valid, and those X such that the inequality ||h¥||X £ C ||F(Sf) ||X{\|{h_{\infty}}\|_{X} \leq C \|{\Phi(Sf)} \|_X} is valid, where Mf and Sf denote the maximal function and the square function of f, respectively. 相似文献
2.
Let j{\varphi} be an analytic self-map of the unit disk
\mathbbD{\mathbb{D}},
H(\mathbbD){H(\mathbb{D})} the space of analytic functions on
\mathbbD{\mathbb{D}} and
g ? H(\mathbbD){g \in H(\mathbb{D})}. The boundedness and compactness of the operator DCj : H¥ ? Z{DC_\varphi : H^\infty \rightarrow { \mathcal Z}} are investigated in this paper. 相似文献
3.
Cristina Fernández-Córdoba Jaume Pujol Mercè Villanueva 《Designs, Codes and Cryptography》2010,56(1):43-59
A code C{{\mathcal C}} is
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive if the set of coordinates can be partitioned into two subsets X and Y such that the punctured code of C{{\mathcal C}} by deleting the coordinates outside X (respectively, Y) is a binary linear code (respectively, a quaternary linear code). The corresponding binary codes of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-additive codes under an extended Gray map are called
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes. In this paper, the invariants for
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the rank and dimension of the kernel, are studied. Specifically, given the algebraic parameters of
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear codes, the possible values of these two invariants, giving lower and upper bounds, are established. For each possible
rank r between these bounds, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with rank r is given. Equivalently, for each possible dimension of the kernel k, the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code with dimension of the kernel k is given. Finally, the bounds on the rank, once the kernel dimension is fixed, are established and the construction of a
\mathbbZ2\mathbbZ4{{\mathbb{Z}_2\mathbb{Z}_4}}-linear code for each possible pair (r, k) is given. 相似文献
4.
Yong-Kum Cho Sunggeum Hong Joonil Kim Chan Woo Yang 《Integral Equations and Operator Theory》2009,65(4):485-528
Given
W ì \mathbbZ+3\Omega \subset {\mathbb{Z}}_{+}^{3}, we discuss a necessary and sufficient condition that the triple Hilbert transform associated with any polynomial of the
form ($t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m$t_1, t_2, t_3,\sum_{m
\in \Omega} a_{m} t^m) is bounded in
Lp(\mathbbR4)L^p({\mathbb{R}}^4). 相似文献
5.
Raymond Mortini 《Complex Analysis and Operator Theory》2011,5(1):219-235
We study the class of inner functions Q{\Theta} whose zero set Z(Q){Z(\Theta)} stays hyperbolically close to
[`(Z\mathbbD(Q))]{\overline{Z_\mathbb{D}(\Theta)}} on the corona of H
∞ and show that these functions are uniformly approximable by interpolating Blaschke products. 相似文献
6.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}Let
G < SL(2, \mathbb Z){\Gamma < {\rm SL}(2, {\mathbb Z})} be a free, finitely generated Fuchsian group of the second kind with no parabolics, and fix two primitive vectors
v0, w0 ? \mathbb Z2 \ {0}{v_{0}, w_{0} \in \mathbb {Z}^{2} \, {\backslash} \, \{0\}}. We consider the set S{\mathcal {S}} of all integers occurring in áv0g, w0?{\langle v_{0}\gamma, w_{0}\rangle}, for g ? G{\gamma \in \Gamma} and the usual inner product on
\mathbb R2{\mathbb {R}^2}. Assume that the critical exponent δ of Γ exceeds 0.99995, so that Γ is thin but not too thin. Using a variant of the circle method, new bilinear forms estimates
and Gamburd’s 5/6-th spectral gap in infinite-volume, we show that S{\mathcal {S}} contains almost all of its admissible primes, that is, those not excluded by local (congruence) obstructions. Moreover, we
show that the exceptional set
\mathfrak E(N){\mathfrak {E}(N)} of integers |n| < N which are locally admissible (n ? S (mod q) for all q 3 1){(n \in \mathcal {S} \, \, ({\rm mod} \, q) \, \, {\rm for\,all} \,\, q \geq 1)} but fail to be globally represented, n ? S{n \notin \mathcal {S}}, has a power savings,
|\mathfrak E(N)| << N1-e0{|\mathfrak {E}(N)| \ll N^{1-\varepsilon_{0}}} for some ${\varepsilon_{0} > 0}${\varepsilon_{0} > 0}, as N → ∞. 相似文献
7.
Let ${\mathcal{P}_{d,n}}Let Pd,n{\mathcal{P}_{d,n}} denote the space of all real polynomials of degree at most d on
\mathbbRn{\mathbb{R}^n} . We prove a new estimate for the logarithmic measure of the sublevel set of a polynomial P ? Pd,1{P\in \mathcal{P}_{d,1}} . Using this estimate, we prove that
supP ? Pd,n| p.v.ò\mathbbRneiP(x)\fracW(x/|x|)|x|ndx| £ c log d (||W||L logL(Sn-1)+1),\mathop{\rm sup}\limits_ {P \in \mathcal{P}_{d,n}}\left| p.v.\int_{\mathbb{R}^{n}}{e^{iP(x)}}{\frac{\Omega(x/|x|)}{|x|^n}dx}\right | \leq c\,{\rm log}\,d\,(||\Omega||_L \log L(S^{n-1})+1), 相似文献
8.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}
9.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
10.
Liviu I. Ignat Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,170(1):918-925
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely,
u¢n(t) = ?j ? \mathbbZd Jn-juj(t)-un(t)u^{\prime}_{n}(t) = \sum_{{j\in}{{{\mathbb{Z}}}^{d}}} J_{n-j}u_{j}(t)-u_{n}(t) with t ≥ 0 and
n ? \mathbbZdn \in {\mathbb{Z}}^{d}. We assume that J is nonnegative and verifies
?n ? \mathbbZdJn = 1\sum_{{n \in {\mathbb{Z}}}^{d}}J_{n}= 1. We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform. 相似文献
11.
Let X be a normed space and V be a convex subset of X. Let a\colon \mathbbR+ ? \mathbbR+{\alpha \colon \mathbb{R}_+ \to \mathbb{R}_+}. A function f \colon V ? \mathbbR{f \colon V \to \mathbb{R}} is called α-midconvex if
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