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1.
Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JNcon(p,q,s) over Rn or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rn or a given cube of Rn with finite side length.Furthermore, some VMO-H1-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results. 相似文献
2.
3.
Xing?Fu Dachun?YangEmail author Yiyu?Liang 《Journal of Fourier Analysis and Applications》2017,23(4):919-990
Let \(({\mathcal X},d,\mu )\) be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and \(H^1_\mathrm{at}({\mathcal X})\) be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hytönen, the authors prove that the product \(f\times g\) of \(f\in H^1_\mathrm{at}({\mathcal X})\) and \(g\in \mathrm {BMO}({\mathcal X})\), viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from \(H^1_\mathrm{at}({\mathcal X})\times \mathrm {BMO}({\mathcal X})\) into \(L^1({\mathcal X})\) and from \(H^1_\mathrm{at}({\mathcal X}) \times \mathrm {BMO}({\mathcal X})\) into \(H^{\log }({\mathcal X})\), which affirmatively confirms the conjecture suggested by A. Bonami and F. Bernicot (This conjecture was presented by Ky in J Math Anal Appl 425:807–817, 2015). 相似文献
4.
5.
自然对流边界层中湍流的发生 总被引:1,自引:0,他引:1
自然对流边界层中从层流到湍流的转捩经历了浮力振型、无摩擦振型和黏性振型的三重流动不稳定性相继产生的前转捩过程,以及近壁迅速出现强湍流源,随之平缓地向自模拟的湍流边界层过渡的热转捩过程.浮力振型在修正Grashof数G>40时开始失稳并成为主要振型,在振幅分布中3种振型的临界层位置处出现3个峰值;在G>100时浮力振型消失,无摩擦振型失稳并成为主要振型,振幅分布中在近壁区还出现黏性振型的峰值;在G>170时无摩擦振型经非线性演化在外层形成较弱的湍流,但内层黏性应力仍远高于湍流应力,振幅分布中仅有与黏性振型相应的峰值,在频谱中黏性振型的基频、第一、第二、第三阶亚谐频随G的增加相继出现,此时黏性不稳定波的高频成分已转化为湍流,但低频成分仍按线性规律增长,直至湍流惯性子区开始形成;至G>800时黏性振型消失,并在G=850附近时近壁区出现强湍流源,湍流应力、湍能产生项和近壁湍流热流率剧增.在热转捩后期,湍流应力和湍能产生项明显下降,流动在内外层趋于平衡. 相似文献
6.
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and the associated Hardy-type space. In this article, we first establish the finite atomic characterization of . As an application, we prove that the dual space of is the Campanato space associated with X. For any given and , using the atomic and the Littlewood–Paley function characterizations of ,we also establish its s-order intrinsic square function characterizations, respectively, in terms of the intrinsic Lusin-area function ,the intrinsic g-function ,and the intrinsic -function , where λ coincides with the best known range. 相似文献
7.
Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted Lp(X) estimate with general weights and a weak type endpoint estimate with A1(X) weights are established for maximal operators corresponding to commutators of BMO(X) functions and singular integral operators with non-smooth kernels. 相似文献
8.
Let p∈(0,1] and s≥[n(1/p−1)], where [n(1/p−1)] denotes the maximal integer no more than n(1/p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H
p
(ℝ
n
) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.
相似文献
9.
Let dγ(x) ≡ π
−n/2
e
−|x|
2
dx for all x ∈ ℝ
n
be the Gauss measure on ℝ
n
. In this paper, the authors establish the characterizations of the space BMO(γ) of Mauceri and Meda via commutators of either local fractional integral operators or local fractional maximal operators.
To this end, the authors first prove that such a local fractional integral operator of order β is bounded from L
p
(γ) to L
p/(1−pβ)(γ), or from the Hardy space H
1(γ) of Mauceri and Meda to L
1/(1−β)(γ) or from L
1/β
(γ) to BMO(γ), where β ∈ (0, 1) and p ∈ (1, 1/β). 相似文献
10.
In this paper,the authors characterize the inhomogeneous Triebel-Lizorkin spaces Fp,q s,w(Rn)with local weight w by using the Lusin-area functions for the full ranges of the indices,and then establish their atomic decompositions for s ∈ R,p ∈(0,1] and q ∈ [p,∞).The novelty is that the weight w here satisfies the classical Muckenhoupt condition only on balls with their radii in(0,1].Finite atomic decompositions for smooth functions in Fp,q s,w(Rn)are also obtained,which further implies that a(sub)linear operator that maps smooth atoms of Fp,q s,w(Rn)uniformly into a bounded set of a(quasi-)Banach space is extended to a bounded operator on the whole Fp,q s,w(Rn).As an application,the boundedness of the local Riesz operator on the space Fp,q s,w(Rn)is obtained. 相似文献