<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> estimates for oscillatory singular integral operators with analytic phrases

L ² estimates are obtained for some oscillatory singular integral operators with analytic phrases by using the technology of almost orthogonality, oscillatory estimates and size estimates.     

Weighted estimates for commutators of one-sided oscillatory integral operators

In this paper, we study the weighted norm inequalities for commutators formed by a class of one-sided oscillatory integral operators and functions in one-sided BMO spaces.     

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.     

Estimates for oscillatory strongly singular integral operators

In this paper we consider oscillatory integral operators with strong singularities on . We obtain sharp decay estimates for L² operator norm. We also obtain H^p estimates for difference of oscillatory strongly singular integral operators and strongly singular integral operators, which gives L^p mapping properties of oscillatory strongly singular integral operators.     

一类奇异积分算子的Toeplitz算子的双权估计

研究了与满足变形L~r-Hormander条件的奇异积分算子和加权Lipschitz函数生成的Toeplitz算子T_b的sharp极大函数的点态估计,并应用该点态估计证明了Toeplitz算子T_b是从L~p(w)到L~q(w~(1-q))上的有界算子;此外还建立了与变形Lipschitz条件的奇异积分算子和加权BMO函数相关的Toeplitz算子T_b的sharp极大函数的点态估计,证明了这类Toeplitz算子是从L~p(μ)到L~q(v)上的有界算子.     

Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces

In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel (x) satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.     

Rough oscillatory singular integral operators of nonconvolution type

In this paper, we study a classes of oscillatory singular integral operators of nonconvolution type with phases more general than polynomials. We prove that such operators are bounded on Lp provided their kernels satisfy a very weak condition. In addition, we also study the related truncated oscillatory singular integral operators. Moreover, we present a class of unbounded oscillatory singular integral operators.     

Weighted estimates for commutators of singular integral operators with non-smooth kernels

In this paper, we establish the boundedness of commutators of singular integral operators with non-smooth kernels on weighted Lipschitz spaces Lipβ,ω. The condition on the kernel in this paper is weaker than the usual pointwise H¨ormander condition.     

Two-weight estimates for singular and strongly singular integral operators

We give a Pontryagin-Thom type construction for Stein factorizations of fold maps of 3-manifolds into the plane. As an application, we compute the cobordism group of Stein factorizations of fold maps of oriented 3-manifolds into the plane and the oriented cobordism group of fold maps of 3-manifolds into the plane. It turns out that these two groups are isomorphic to Z ₂ ⊕ Z ₂. We have the analogous results about bordism groups as well.      

Weighted norm inequalities with multiple-weight for singular integral operators with non-smooth kernels

By sharp maximal function, we establish a weighted estimate with multiple-weight for the multilinear singular integral operators with non-smooth kernels.     

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.     

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.     

Weighted estimates for commutators of singular integral operators with non-doubling measures

Letμbe a nonnegative Radon measure on R~d which only satisfiesμ(B(x,r))≤C_0r~n for all x∈R~d,r>0,and some fixed constants C_0>0 and n∈(0,d].In this paper,some weighted weak type estimates with A_(p,(log L)~σ)~ρ(μ) weights are established for the commutators generated by Calder■n-Zygmund singular integral operators with RBMO(μ) functions.     

A priori estimates for one-dimensional singular integral operators with continuous coefficients

Let the contour γ consist of a finite number of simple closed pairwise nonintersecting curves, satisfying a Lyapunov condition, let S be the operator of singular integration in spacel _p , (γ) (1 <p < ∞), and leta (t), b (t) εC (γ) 1 <p ₁. <p < ∞. The necessary and sufficient condition for A = aI+ bS to be a Φ-operator in space L_p(γ) is that, for all?ε L_p(γ), ∥?∥_p ? const (∥ A?_p + ∥ ? ∥_p1), where ∥?∥_p = ∥?∥L_p (γ).     

Weighted estimates for the multilinear singular integral operators with non-smooth kernels

In this paper, by sharp function estimates and certain weak type endpoint estimates, the authors establish some weighted norm inequalities with Ap weights for the multilinear singular integral operators with non-smooth kernels.     

Maximal bilinear singular integral operators associated with dilations of planar sets

We obtain square function estimates and bounds for maximal singular integral operators associated with bilinear multipliers given by characteristic functions of dyadic dilations of certain planar sets. As a consequence, we deduce pointwise almost everywhere convergence for lacunary partial sums of bilinear Fourier series with respect to methods of summation determined by the corresponding planar sets.     

Lack of natural weighted estimates for some singular integral operators

We show that the classical Hörmander condition, or analogously the -Hörmander condition, for singular integral operators is not sufficient to derive Coifman's inequality

where , is the Hardy-Littlewood maximal operator, is any weight and is a constant depending upon and the constant of . This estimate is well known to hold when is a Calderón-Zygmund operator.

As a consequence we deduce that the following estimate does not hold:

where and where is an arbitrary weight. However, by a recent result due to A. Lerner, this inequality is satisfied whenever is a Calderón-Zygmund operator.

One of the main ingredients of the proof is a very general extrapolation theorem for weights.

     

Weighted estimates for singular integral operators and commutators associated with the sections

In this paper we prove weighted estimates for singular integral operators and commutators associated with the sections.     

Weak estimates for commutators of fractional integral operators

By introducing a kind of maximal operator of the fractional order associated with the mean Luxemburg norm and using the technique of the sharp function, the weak type LlogL estimates for the commutators of the fractional integral operator and the related maximal operator are established.