A BMO estimate for the multilinear singular integral operator

The behavior on the space L∞((R)n) for the multilinear singular integral operator defined by TAf(x)=∫Rn Ω(x-y)/|x-y|n 1(A(x)-A(y)-(△)A(y)(x-y))f(y)dy is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO((R)n). It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L∞((R)n), TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO((R)n).     

On boundedness of discrete multilinear singular integral operators

Let m(ξ,η) be a measurable locally bounded function defined in R². Let 1?p₁,q₁,p₂,q₂<∞ such that pi=1 implies qi=∞. Let also 0<p₃,q₃<∞ and 1/p=1/p₁+1/p₂−1/p₃. We prove the following transference result: the operator

     

On the scaling limit of a singular integral operator

The scaling limit and Schauder bounds are derived for a singular integral operator arising from a difference equation approach to monodromy problems. Research supported in part by National Science Foundation grants DMS-02-45371 and DMS-04-05519.     

Maximal operator for multilinear Calderón-Zygmund singular integral operators on weighted Hardy spaces

In this paper, the maximal operator associated with multilinear Calderón-Zygmund singular integral operators will be studied by using an improved Coltlar's inequality. Moreover, weighted norm inequalities and some estimates on weighted Hardy spaces are obtained for this maximal operator.     

Estimates for the maximal multilinear singular integral operators

In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the Lp(Rn) (1 < p < ∞) boundedness and a weak type L log L estimate for the corresponding maximal operator.     

A note on the multilinear singular integral operators

Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 ＜α≤ 1) and implies the Lp(Rn) (1 ＜ p ＜ oo) boundedness for the operator TA. Some endpoint estimates are also established.     

Weighted Morrey spaces and a singular integral operator

In this paper, we shall introduce a weighted Morrey space and study the several properties of classical operatorsin harmonic analysis on this space (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Bergman projection as a singular integral operator

We show that the Bergman projection operator, associated to one of three classes of domains (all smoothly bounded)-a finite type domain ?²; a decoupled, finite type domain in ?ⁿ; or a convex, finite type domain in wfⁿ-may be viewed as a generalized Calderón-Zygmund operator. As an application of this observation, we show that the Bergman projector on any of these domains preserves the Lebesgue classesL ^p , 1 <p < ∞.     

Some BMO estimates for vector-valued multilinear singular integral operators

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.     

A sharp function estimate for multilinear singular integral operators

A variant sharp function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given. Supported by the NSF of China (19701039)     

Pointwise estimates for the maximal multilinear singular integral operators

Two pointwise estimates relating the maximal multilinear singular integral operators and some classical maximal operators are established. These pointwise estimates imply the rearrangement estimate and the BLO(Rn) estimate for the maximal multilinear singular integral operators.     

Estimates for multilinear singular integral operators with nonsmooth kernels

Let (, d, μ) be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, we consider the behavior on × ⋯ × for the m-linear singular integral operators with nonsmooth kernels which were first introduced by Duong, Grafakos and Yan.     

Weighted estimate for the multilinear oscillatory singular integral operators

In this paper, the weighted L^p(R^n) boundedness for the multilinear oscillatory singular integral operators with polynomial phases is studied.     

A sharp function estimate for multilinear singular integral operators

A variant sharp function estimate is established for the multilinear singular integral operators. Two applications of this estimate are also given.     

An endpoint estimate for maximal multilinear singular integral operators

A weak type endpoint estimate for the maximal multilinear singular integral operator T*Af(x)=supε＞0|(f)(x-y)＞ε (Ω(x-y)/(|x-y|(n 1)))(A(x)-A(y)-▽A(y)(x-y))f(y)dy| is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO(Rn). A regularity condition on Ω which implies an LlogL type estimate of T*A is given.     

Two problems about singular integral operator

In this paper we consider L² bounds and weak type (1.1) bounds for a class of singular integral operators introduced by R. Fefferman and Namazi. Then, we solve two problems proposed by Shi.     

On a singular differential operator

Summary Study of the properties of a singular differential operator in one independent variable. Applications to ordinary and partial differential equations. To Giovanni Sansone on his 70^th birth day. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under Contract No. 49 (638)-228.     

Estimate for a class of multilinear fractional integral operator with rough kernel

In this paper, we prove the boundedness from H1(Rn) to L n/n-α ,∞(Rn) for the multilinear fractional integral operator with rough kernel related to the mi-th remainder of Taylor series of Ai at x about y for i = 1,2, ,l.