arXiv 0909.32312009-09-17math.FA

A framework for non-homogeneous analysis on metric spaces, and the RBMO space of Tolsa

Tuomas P. Hytönen

备注：: 12 pages, submitted

英文摘要：

A new class of metric measure spaces is introduced and studied. This class generalises the well-established doubling metric measure spaces as well as the spaces (R^n,mu) with mu(B(x,r))<Cr^d, in which non-doubling harmonic analysis has recently been developed. It seems to be a promising framework for an abstract extension of this theory. Tolsa's space of regularised BMO functions is defined in this new setting, and the John-Nirenberg inequality is proven.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Calderón-Zygmund operators on RBMO

Let $μ$ be an $n$-dimensional finite positive measure on $\mathbb{R}^m$. We obtain a $T1$ condition sufficient for the boundedness of Calderón-Zygmund operators on $\textrm{RBMO}(μ)$, the regular BMO space of Tolsa.

2021-06-01math.CAmath.FA

Calderón-Zygmund算子在RBMO上的一个刻画

A characterization of Calderón-Zygmund operators on RBMO

本文针对$\mathbb{R}^m$上非 doubling 测度引入的 RBMO 空间，利用函数 $T1$ 给出了有界 Calderón-Zygmund 算子的一个刻画。

2024-06-05math.CAmath.FA

BMO from dyadic BMO for nonhomogeneous measures

The usual one third trick allows to reduce problems involving general cubes to a countable family. Moreover, this covering lemma uses only dyadic cubes, which allows to use nice martingale properties in harmonic analysis problems. We consider alternatives to this technique in spaces equipped with nonhomogeneous measures. This entails additional difficulties which forces us to consider martingale filtrations that are not regular. The dyadic covering that we find can be used to clarify the relationship between martingale BMO spaces and the most natural BMO space in this setting, which is the spa…

2018-06-27math.CAmath.FA

Commutators of multilinear strongly singular integrals on non-homogeneous metric measure spaces

Let $(X,d,μ)$ denotes non-homogeneous metric measure space satisfying geometrically doubling and the upper doubling measure condition. In this paper, the boundedness in Lebesgue spaces for two kinds of commutators, which are iterated commutators and commutators in summation form, generated by multilinear strongly singular integral operators with RBMO$(μ)$ function on non-homogeneous metric measure spaces $(X,d,μ)$ is obtained.

2021-10-25math.FA

Commutators of multilinear singular integral operators on non-homogeneous metric measure spaces

Let $(X,d,μ)$ be a metric measure space satisfying both the geometrically doubling and the upper doubling measure conditions, which is called non-homogeneous metric measure space. In this paper, via a sharp maximal operator, the boundedness of commutators generated by multilinear singular integral with $RBMO(μ)$ function on non-homogeneous metric measure spaces in $m$-multiple Lebesgue spaces is obtained.

2014-04-22math.FA

Boundedness of fractional integral operators on non-homogeneous metric measure spaces

In this paper, the fractional integral operator on non-homogeneous metric measure spaces is introduced, which contains the classic fractional integral operator, fractional integral with non-doubling measures and fractional integral with fractional kernel of order $α$ and regularity $ε$ introduced by García-Cuerva and Gatto as special cases. And the $(L^{p}(μ),L^{q}(μ))$-boundedness for fractional integral operators on non-homogeneous metric measure spaces is established. From this, the $(L^{p}(μ),L^{q}(μ))$-boundedness for commutators and multilinear commutators generated by fractional integra…

2013-09-26math.FA

更多相关论文收起更多论文

Boundedness of Commutators on Hardy Spaces over Metric Measure Spaces of Non-homogeneous Type

Let $(\mathcal{X},d,μ)$ be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. Let $T$ be a Calderón-Zygmund operator with kernel satisfying only the size condition and some Hörmander-type condition, and $b\in\rm{\widetilde{RBMO}(μ)}$ (the regularized BMO space with the discrete coefficient). In this paper, the authors establish the boundedness of the commutator $T_b:=bT-Tb$ generated by $T$ and $b$ from the atomic Hardy space $\widetilde{H}^1(μ)$ with the discrete coefficient into the weak Lebesgue space $L^{1,\,\infty}(μ)$. The b…

2015-09-18math.CAmath.FA

Equivalent boundedness of Marcinkiewicz integrals on non-homogeneous metric measure spaces

Let $({\mathcal X},\,d,\,μ)$ be a metric measure space satisfying the upper doubling condition and the geometrically doubling condition in the sense of T. Hytönen. In this paper, the authors prove that the $L^p(μ)$ boundedness with $p\in(1,\,\infty)$ of the Marcinkiewicz integral is equivalent to either of its boundedness from $L^1(μ)$ into $L^{1,\infty}(μ)$ or from the atomic Hardy space $H^1(μ)$ into $L^1(μ)$. Moreover, the authors show that, if the Marcinkiewicz integral is bounded from $H^1(μ)$ into $L^1(μ)$, then it is also bounded from $L^\infty(μ)$ into the space ${\mathop\mathrm{RBLO}}…

2013-08-27math.CAmath.FA

Generalized Fractional Integrals and Their Commutators over Non-homogeneous Metric Measure Spaces

Let $({\mathcal X},d,μ)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional integrals over $({\mathcal X},d,μ)$. The authors also prove that multilinear commutators of fractional integrals with ${\mathop\mathrm{\,RBMO(μ)}}$ functions are bounded on Orlicz spaces over $({\mathcal X},d,μ)$, which include Lebesgue spaces as special cases. The weak type endpoint estimates for multilinear commutators of fractional integrals with functions in t…

2014-01-29math.CAmath.FA

Hardy spaces, Regularized BMO spaces and the boundedness of Calderón-Zygmund operators on non-homogeneous spaces

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 a Calderón-Zygmund operator $T$ as well as the boundedness of certain related singular integrals associated with $T$ 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 \cite{T1} on the non-homogeneous space $(\mathbb R^n…

2011-08-27math.FA