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1.
One defines a non-homogeneous space (X,μ) as a metric space equipped with a non-doubling measure μ so that the volume of the ball with center x, radius r has an upper bound of the form r n for some n>0. The aim of this paper is to study the boundedness of Calderón–Zygmund singular integral operators T on various function spaces on (X,μ) such as the Hardy spaces, the L p spaces, and the regularized BMO spaces. This article thus extends the work of X. Tolsa (Math. Ann. 319:89–149, 2011) on the non-homogeneous space (? n ,μ) to the setting of a general non-homogeneous space (X,μ). Our framework of the non-homogeneous space (X,μ) is similar to that of Hytönen (2011) and we are able to obtain quite a few properties similar to those of Calderón–Zygmund operators on doubling spaces such as the weak type (1,1) estimate, boundedness from Hardy space into L 1, boundedness from L into the regularized BMO, and an interpolation theorem. Furthermore, we prove that the dual space of the Hardy space is the regularized BMO space, obtain a Calderón–Zygmund decomposition on the non-homogeneous space (X,μ), and use this decomposition to show the boundedness of the maximal operators in the form of a Cotlar inequality as well as the boundedness of commutators of Calderón–Zygmund operators and BMO functions.  相似文献   

2.
In this paper, the authors introduce Morrey-type spaces on the locally doubling metric measure spaces, which means that the underlying measure enjoys the doubling and the reverse doubling properties only on a class of admissible balls, and then obtain the boundedness of the local Hardy–Littlewood maximal operator and the local fractional integral operator on such Morrey-type spaces. These Morrey-type spaces on the Gauss measure space are further proved to be naturally adapted to singular integrals associated with the Ornstein–Uhlenbeck operator. To be precise, by means of the locally doubling property and the geometric properties of the Gauss measure, the authors establish the equivalence between Morrey-type spaces and Campanato-type spaces on the Gauss measure space, and the boundedness for a class of singular integrals associated with the Ornstein–Uhlenbeck operator (including Riesz transforms of any order) on Morrey-type spaces over the Gauss measure space.  相似文献   

3.
陶双平  逯光辉 《数学学报》2019,62(2):269-278
本文建立了 Marcinkiewicz 积分M与具离散系数的正则有界平均振荡空间RBMO(μ)生成的交换子Mb在非齐性度量测度空间上的有界性. 在控制函数λ满足∈-弱反双倍条件的假设下, 当p∈(1,∞)时,证明了Mb在Lp(μ)上是有界的. 另外,还得到了Mb在 Morrey 空间上的有界性.  相似文献   

4.
We consider a Poisson process ?? on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of ??. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener?CIt? chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincaré inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris?CFKG-inequalities for monotone functions of ??.  相似文献   

5.
We show that a domain is an extension domain for a Haj?asz–Besov or for a Haj?asz–Triebel–Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are replaced by median values, which allows us to handle also the case \(0<p<1\). The necessity of the measure density condition is derived from embedding theorems; in the case of Haj?asz–Besov spaces we apply an optimal Lorentz-type Sobolev embedding theorem which we prove using a new interpolation result. This interpolation theorem says that Haj?asz–Besov spaces are intermediate spaces between \(L^p\) and Haj?asz–Sobolev spaces. Our results are proved in the setting of a metric measure space, but most of them are new even in the Euclidean setting, for instance, we obtain a characterization of extension domains for classical Besov spaces \(B^s_{p,q}\), \(0<s<1\), \(0<p<\infty \), \(0<q\le \infty \), defined via the \(L^p\)-modulus of smoothness of a function.  相似文献   

6.
By taking an interest in a natural extension to the small parameters of the trace inequality for Morrey spaces, Orlicz–Morrey spaces are introduced and some inequalities for generalized fractional integral operators on Orlicz–Morrey spaces are established. The local boundedness property of the Orlicz maximal operators is investigated and some Morrey-norm equivalences are also verified. The result obtained here sharpens the one in our earlier papers.  相似文献   

7.
The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,Iγ]which is generated by fractional integral Iγand function b∈Lipβ(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,Iγ]is compact from Morrey space Mqp(μ)into Morrey space Mts(μ)if and only if b∈Lipβ(μ).  相似文献   

8.
Vector-valued fractional maximal inequalities on variable Morrey spaces are proved. Applying atomic decomposition of variable Hardy–Morrey spaces, we obtain the boundedness of fractional integrals on variable Hardy–Morrey spaces, which extends the Taibleson–Weiss’s results for the boundedness of fractional integrals on Hardy spaces. The corresponding boundedness for the fractional type integrals is also considered.  相似文献   

9.
In this paper, the authors study the boundedness of multilinear fractional integrals on the product Morrey space with non-doubling measure, and investigate the Morrey boundedness properties of the multilinear commutators generated by multilinear fractional integral operators with a tuple of RBMO functions.  相似文献   

10.
In this article, the authors establish several equivalent characterizations of fractional Haj?asz-Morrey-Sobolev spaces on spaces of homogeneous type in the sense of Coifman and Weiss.  相似文献   

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