共查询到20条相似文献,搜索用时 0 毫秒
1.
Eiichi Nakai 《Mathematische Nachrichten》1994,166(1):95-103
Any continuous linear operator T: Lp → Lq has a natural vector-valued extension T: Lp(l) → Lq(l) which is automatically continuous. Relations between the norms of these operators in the cases of p = q and r = 2 were considered by Marcinkiewicz -Zygmund [28], Herz [14] and Krivine [19] - [21]. In this paper we study systematically these relations and given some applications. It turns out that some known results can be proved in a simple way as a consequence of these developments. 相似文献
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We study the boundedness of the HardyLittlewood maximalfunction in weighted Lorentz spaces, using some new techniqueson distribution and rearrangement functions. Our goal is togive a unified version of some well-known weighted inequalitiesin Rn and R+, showing the relation between the theories. 相似文献
5.
SL(2,R)上的Hardy-Littlewood极大函数 总被引:1,自引:0,他引:1
给出了SL(2 ,R)上的Hardy Littlewood极大函数mf 和局部Hardy Littlewood极大函数mRf 的定义 ,对f∈L1(G) ,我们得到了 | {g∈SL(2 ,R) |mf(g) >λ} |的估计 ,且证明了局部Hardy Littlewood极大函数的弱(1.1)型和强 (p ,p)型 ,p >1. 相似文献
6.
I. A. Ikromov 《Mathematical Notes》2005,78(5-6):773-790
In the present paper, we consider estimates of the Fourier transform of Borel measures concentrated on analytic hypersurfaces and containing a mitigating factor. The mitigating factors are expressed in terms of principal curvatures of the surface. The resulting estimates are applied to investigating the boundedness of the corresponding maximal operators. 相似文献
7.
广义模糊数值Choquet积分的伪自连续及其遗传性 总被引:3,自引:0,他引:3
在广义模糊测度空间上,针对已经给出的广义模糊数值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,研究当模糊测度满足伪自连续、伪一致自连续性时,这种模糊数值Choquet积分所保持的一些遗传性. 相似文献
8.
Ron Dror Suman Ganguli Robert S. Strichartz 《Journal of Fourier Analysis and Applications》1995,2(5):473-486
Let
be the centered maximal operator on the line. Through a numerical search procedure, we have conjectural best constants for
the weak-type 1-1 estimate (3/2) and the Lp estimate (the constant B(p,1) such that
We prove that these constants are lower bounds for the best constants and discuss the numerical evidence for the conjectures. 相似文献
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模糊积分变换与模糊Choquet积分的一致连续性 总被引:2,自引:0,他引:2
在一般非负单调函数空间 m[0 ,a]上引入模糊积分变换与距离的概念 ,证明了这种模糊积分变换与模糊 Choquet积分在 m[0 ,a]上关于这种距离是一致连续的 ,从而说明当 m[0 ,a]上两个函数变化不大时 ,不会使相应的模糊积分变换与模糊 Choquet积分产生较大的变化 . 相似文献
10.
I. A. Ikromov 《Functional Analysis and Its Applications》2005,39(2):140-143
Let S ⊂ ℝR
n +1 be a real-analytic hypersurface with surface measure dσ, and let ψ be a smooth nonnegative compactly supported cutoff function. Consider the surface measure dμ q = ψ|Λ(X)|q
dσ, where Λ(X) is a damping factor determined by the matrices of the first and second fundamental forms of the surface. We show that its Fourier transform
decays for large |ξ| as O (|ξ|−(1/2+ε)), ε > 0, provided that q > 3/2. We also consider applications involving maximal operators associated with means of functions over hypersurfaces.__________Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 39, No. 2, pp. 70–74, 2005Original Russian Text Copyright © by I. A. Ikromov 相似文献
11.
广义模糊数值Choquet积分的自连续性与其结构特征的保持 总被引:10,自引:1,他引:10
在一般模糊测度空间的任一子集上,针对给定的μ-可积数模糊数值函数,定义所谓广义的模糊数值Choquet积分,并将这种积分整体看成可测空间上的模糊数值集函数.进而讨论并研究它的上(下)自连续性,逆上(下)自连续性,一致自连续性和一致逆自连续性等结构特征. 相似文献
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Kim Weon-Ju; Wainger Stephen; Wright James; Ziesler Sarah 《Bulletin London Mathematical Society》1996,28(3):291-296
We obtain Lp estimates for singular integrals and maximal functionsassociated to hypersurfaces in Rn+1, n 2, which are obtainedby rotating a curve around one of the coordinate axes. 相似文献
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In an abstract set up, we get strong type inequalities in L~(p+1) by assuming weak or extra-weak inequalities in Orlicz spaces. For some classes of functions, the number p is related to Simonenko indices. We apply the results to get strong inequalities for maximal functions associated to best Φ-approximation operators in an Orlicz space L~Φ. 相似文献
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研究中心Kakeya(Nikodym)极大算子K_N(N2)及其分数次情形K_(α,N)(0αd)的正则性.特别地,建立了中心分数次Kakeya极大算子K_(α,N)是从W~(1,p)(R~d)到W~(1,q)(R~d)上的有界连续算子,其中1p∞,q=dp/(d-αp)和0≤αd/p.还证明了中心Kakeya极大算子K_N是分数次Sobolev空间W~(s,p)(R~d),非齐次Triebel-Lizorkin空间F_s~(p,q)(R~d)以及非齐次Besov空间B_s~(p,q)(R~d)上的有界连续算子,其中0s1,1p,q∞.此外,也考虑分数次Kakeya极大函数的弱导数的两种点态估计以及其离散情形的正则性. 相似文献
16.
Hitoshi Tanaka 《数学学报(英文版)》2002,18(3):447-454
Let K
δ, 0 < δ≪1, be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity δ. The (so-called)
Fefferman-Stein-type inequality: is shown, where C
d
and α
d
are constants depending only on the dimension d and w is a weight. The result contains the exponent (d−2)/2d which is smaller than the exponent (d−2)(d−1)/d(2d−3) obtained in [7].
Received October 8, 2001, Accepted February 28, 2002 相似文献
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李艳红 《数学的实践与认识》2008,38(5):158-162
针对模糊测度空间上已建立的模糊值Choquet积分,将这种积分整体看成可测空间上取值于模糊数的集函数,当模糊测度满足一般S性和PGP性时,研究了这种模糊值集函数所保持的遗传性质. 相似文献
18.
Eleftherios N. Nikolidakis 《Journal of Fourier Analysis and Applications》2013,19(1):115-139
We obtain sharp estimates for the localized distribution function of $\mathcal{M}\phi $ , when ? belongs to L p,∞ where $\mathcal{M}$ is the dyadic maximal operator. We obtain these estimates given the L 1 and L q norm, q<p and certain weak-L p conditions.In this way we refine the known weak (1,1) type inequality for the dyadic maximal operator. As a consequence we prove that the inequality 0.1 is sharp allowing every possible value for the L 1 and the L q norm for a fixed q such that 1<q<p, where ∥?∥ p,∞ is the usual quasi norm on L p,∞. 相似文献
19.
We deal with weighted inequalities of the type [formula] where: T is either the HardyLittlewood maximal operator or asingular integral operator; G is any measurable subset of Rn; f is any measurable function, vanishing outside G, such thatTf is well-defined; v and w are weights, that is, nonnegativelocally integrable functions on G; p, q(1, ). 1991 Mathematics Subject Classification 42B20, 42B25. 相似文献
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It is proved that a cosine operator function C(·), withgenerator A, is locally of bounded semivariation if and onlyif u'(t) = Au(t)+f(t), t>0, u(0), u'(0)D(A), has a strongsolution for every continuous function f, if and only if thefunction , is twice continuously differentiable for every continuous function f, that is, C(·)has the maximal regularity property if and only if A is a boundedoperator. Some other characterisations of bounded generatorsof cosine operator functions are also established in terms oftheir local semivariations. 相似文献