共查询到10条相似文献,搜索用时 78 毫秒
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Ming Ju LIU Shan Zhen LU 《数学学报(英文版)》2007,23(1):7-16
In this paper, the authors study some properties of Littlewood-Paley g-functions gψ(f),Lusin area functions Sψ,α(f) and Littlewood-Paley gψ^*,λ(f) functions defined on H^n, where α,λ 〉 0 and ψ, f are suitable functions. They are the generalization of the corresponding operators on R^n. 相似文献
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R. V. Ambartzumian 《Probability Theory and Related Fields》1976,37(2):145-155
Every c-finite measure Μ on the set G of the lines on the plane such that $$(0){\text{ }}\mu {\text{(\{ g}} \in G:{\text{ }}P \in {\text{g\} ) = 0}}$$ for every point P?R 2 generates a pseudo-metric F on the plane when one puts F P 1, P 2= \(\tfrac{1}{2}\) μ({g∈G:g separates the points P 1 and P 2}) The pseudo-metrics which are generated in this way possess the property of linear additivity, that is F(P 1,P 3)=F(P 1,P 2)+F(P 2,P 3) for P 1,P 2,P 3 on a line, P 2 between P 1 and P 3, and are continuous with respect to the Euclidean topology in R 2 × R 2. In this paper we prove the converse: every linear additive and continuous pseudo-metric F is generated as above by some c-finite measure Μ on G for which (0) holds. The method of proof shows that values of linearly additive and continuous pseudo-metric F inside every bounded convex polygon C are determined completely by the values of F on (δC)2. The representation of pseudo-metrics by measures is useful in derivation of inequalities for the former. 相似文献
4.
WANG Meng CHEN Jiecheng & FAN Dashan Department of Mathematics Zhejiang University 《中国科学A辑(英文版)》2006,49(1):98-108
We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog L(Sn-1 × Sm-1) satisfying the cancellation condition. 相似文献
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Luca Brandolini Marco Magliaro 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2326-2337
This paper deals with the study of differential inequalities with gradient terms on Carnot groups. We are mainly focused on inequalities of the form Δφu≥f(u)l(|∇0u|), where f, l and φ are continuous functions satisfying suitable monotonicity assumptions and Δφ is the φ-Laplace operator, a natural generalization of the p-Laplace operator which has recently been studied in the context of Carnot groups. We extend to general Carnot groups the results proved in Magliaro et al. (2011) [7] for the Heisenberg group, showing the validity of Liouville-type theorems under a suitable Keller-Osserman condition. In doing so, we also prove a maximum principle for inequality Δφu≥f(u)l(|∇0u|). Finally, we show sharpness of our results for a general φ-Laplacian. 相似文献
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Shigeki Akiyama Horst Brunotte Attila Pethő Wolfgang Steiner 《Periodica Mathematica Hungarica》2006,52(1):1-17
Summary The periodicity of sequences of integers <InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource
Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"10"><EquationSource
Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>(a_{n})_{n\in\mathbb
Z}$ satisfying the inequalities <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource
Format="TEX"><![CDATA[$$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation> 0 \le a_{n-1}+\lambda a_n
+a_{n+1} < 1 \ (n \in {\mathbb Z}) $$ is studied for real $ \lambda $ with $|\lambda|< 2$. Periodicity is proved in case $
\lambda $ is the golden ratio; for other values of $ \lambda $ statements on possible period lengths are given. Further interesting
results on the morphology of periods are illustrated. The problem is connected to the investigation of shift radix systems
and of Salem numbers. 相似文献
7.
Let B be the Brownian motion on a noncompact non Euclidean rank one symmetric space H. A typical examples is an hyperbolic space H
n
, n > 2. For ν > 0, the Brownian bridge B
(ν) of length ν on H is the process B
t
, 0 ≤t≤ν, conditioned by B
0 = B
ν = o, where o is an origin in H. It is proved that the process converges weakly to the Brownian excursion when ν→ + ∞ (the Brownian excursion is the radial part of the Brownian Bridge
on ℝ3). The same result holds for the simple random walk on an homogeneous tree.
Received: 4 December 1998 / Revised version: 22 January 1999 相似文献
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Let X be a complex Banach space and let J:XX* be a duality sectionon X (that is, x,J(x)=||J(x)||||x||=||J(x)||2)=||x||2). Forany unit vector x and any (C0) contraction semigroup T={etA:t0}, Goldstein proved that if X is a Hilbert space and |T(t)x,j(x)|1 as t, then x is an eigenvector of A corresponding toa purel imaginary eigenvalue. In this article, we prove thata similar result holds if X is a strictly convex complex Banachspace. 相似文献
10.
Luca Scala 《Geometriae Dedicata》2009,139(1):313-329
We study tautological sheaves on the Hilbert scheme of points on a smooth quasi-projective algebraic surface by means of the
Bridgeland–King–Reid transform. We obtain Brion–Danila’s Formulas for the derived direct image of tautological sheaves or
their double tensor product for the Hilbert–Chow morphism; as an application we compute the cohomology of the Hilbert scheme
with values in tautological sheaves or in their double tensor product, thus generalizing results previously obtained for tautological
bundles.
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