arXiv subjects

Chin-Cheng Lin

Publications and source records attributed to Chin-Cheng Lin.

6 recordsLinked to original sources

arXiv2017

Boundedness of Monge-Ampere singular integral operators on Besov spaces

Let $\phi: \Bbb R^n \mapsto \Bbb R$ be a strictly convex and smooth function, and $\mu= \text{det}\,D^2 \phi$ be the Monge-Amp\`ere measure generated by $\phi.$ For $x\in \Bbb R^n$ and $t>0$, let $S(x,t):=\{y\in \Bbb R^n: \phi(y)<\phi(x)+\nabla \phi(x)\cdot(y-x)+t\}$ denote the section. If $\mu$ satisfies the doubling property, Caffarelli and Guti\'errez (Trans. AMS 348:1075--1092, 1996) provided a variant of the Calder\'on-Zygmund decomposition and a John-Nirenberg-type inequality associated with sections. Under a stronger uniform continuity condition on $\mu$, they also (Amer. J. Math. 119:423--465, 1997) proved an invariant Harnack's inequality for nonnegative solutions of the Monge-Amp\`ere equations with respect to sections. The purpose of this paper is to establish a theory of Besov spaces associated with sections under only the doubling condition on $\mu$ and prove that Monge-Amp\`ere singular integral operators are bounded on these spaces.

math.FA↗

arXiv2017

A class of singular integrals associated with Zygmund dilations

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for these operators on $L^p, 1<p<\infty$, which covers those studied by Ricci--Stein \cite{RS} and Nagel--Wainger \cite{NW}

math.CA↗

arXiv2013

$Tb$ theorem on product spaces

In this paper, we prove a $Tb$ theorem on product spaces $\Bbb R^n\times \Bbb R^m$, where $b(x_1,x_2)=b_1(x_1)b_2(x_2)$, $b_1$ and $b_2$ are para-accretive functions on $\Bbb R^n$ and $\Bbb R^m$, respectively.

math.CA↗

arXiv2012

T1 theorem on product Carnot-Caratheodory spaces

Nagel and Stein established $L^p$-boundedness for a class of singular integrals of NIS type, that is, non-isotropic smoothing operators of order 0, on spaces $\widetilde{M}=M_1\times...\times M_n,$ where each factor space $M_i, 1\leq i\leq n,$ is a smooth manifold on which the basic geometry is given by a control, or Carnot--Carathéodory, metric induced by a collection of vector fields of finite type. In this paper we prove the product $T1$ theorem on $L^2,$ the Hardy space $H^p(\widetilde{M})$ and the space $CMO^p(\widetilde{M})$, the dual of $H^p(\widetilde{M}),$ for a class of product singular integral operators which covers Journé's class and operators studied by Nagel and Stein.

math.FA↗

arXiv2012

Weighted norm inequalities for multilinear singular integral operators and applications

In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r'}$-Hörmander regularity condition. As applications, we recover a weighted estimate for the multilinear Fourier multiplier obtained by Fujita and Tomita, and obtain several new weighted estimates for the multilinear Fourier multiplier as well.

math.FA↗

arXiv2011

Hardy spaces associated with Schrodinger operators on the Heisenberg group

Let $L= -Δ_{\mathbb{H}^n}+V$ be a Schrödinger operator on the Heisenberg group $\mathbb{H}^n$, where $Δ_{\mathbb{H}^n}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse Hölder class $B_{\frac{Q}{2}}$ and $Q$ is the homogeneous dimension of $\mathbb{H}^n$. The Riesz transforms associated with the Schrödinger operator $L$ are bounded from $L^1(\mathbb{H}^n)$ to $L^{1,\infty}(\mathbb{H}^n)$. The $L^1$ integrability of the Riesz transforms associated with $L$ characterizes a certain Hardy type space denoted by $H^1_L(\mathbb{H}^n)$ which is larger than the usual Hardy space $H^1(\mathbb{H}^n)$. We define $H^1_L(\mathbb{H}^n)$ in terms of the maximal function with respect to the semigroup $\big \{e^{-s L}:\; s>0 \big\}$, and give the atomic decomposition of $H^1_L(\mathbb{H}^n)$. As an application of the atomic decomposition theorem, we prove that $H^1_L(\mathbb{H}^n)$ can be characterized by the Riesz transforms associated with $L$. All results hold for stratified groups as well.

math.AP↗