On multiple singular integrals along polynomial curves with rough kernels

This paper is devoted to the study of a class of singular integral operators defined by polynomial mappings on product domains. Some rather weak size conditions, which imply the Lp boundedness of these singular integral operators as well as the corresponding maximal truncated singular integral operators for some fixed 1〈p〈 ∞,are given.     

Singular integrals with rough kernels along real-analytic submanifolds in R n

L ^p mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translated of a real-analytic submanifold in R ⁿ .Work in this paper was done during the second author's visit at the Department of Mathematics, University of Pittsburgh.Supported in part by NSF Grant DMS-9622979.     

Singular integrals along surfaces on product domains

In this paper, we study the mapping properties of singular integral operator along surfaces of revolution. We prove Lp bounds (1 < p < ∞) for such singular integral operators as well as for their corresponding maximal truncated singular integrals if the singular kernels are allowed to be in certain block spaces.     

On Laplacian integrals with singular kernels

A class of Laplace transforms with singular kernels are manipulated into integrls more amenable to analytic evaluation.     

Singular Radon transforms along odd curves on the Heisenberg group

In this article we study the singular integral operators along the curve on the Heisenberg group. It is a variable coefficient extension of the singular integrals along the odd curves on the Euclidean space ℝ². The proof is based on the generalized Calderon-Zygmund theory on the space of homogeneous type.     

全纯函数的加权积分

§ 1　 IntroductionLet D be the unit disc in the complex plane C,dm be the Lebesgue area measure onD.We denote H (D) the setof all holomorphic functions on D.For 0 相似文献   

Singular convolution integrals with operator-valued kernel

We study operators \(f\mapsto Kf\) of the form \((Kf)(t)=\int_{{\bf R}^{n}} k(t-s)f(s) {\rm d}s\), where f is a vector-valued function and k an operator-valued singular kernel. Sufficient conditions for boundedness on L ^p -spaces of UMD-valued functions are given in terms of a Hörmander-type condition involving R-boundedness. The results cover large classes of kernels and also provide new proofs of recent operator-valued Fourier multiplier theorems. Moreover, they give new information about families of singular integral operators.     

Invariant algebraic curves and rational first integrals of holomorphic foliations in CP(2)

In this paper, using the tools of algebraic geometry we provide sufficient conditions for a holomor-phic foliation in CP(2) to have a rational first integral. Moreover, we obtain an upper bound of the degrees of invariant algebraic curves of a holomorphic foliation in CP(2). Then we use these results to prove that any holomorphic foliation of degree 2 does not have cubic limit cycles.     

Weighted Lp-estimates for singular integrals with anisotropic kernels

One gives a generalization of Muckenhoupt's theorem to the case of anisotropic singular integrals, in particular, integrals whose kernels are the derivatives of the fundamental solutions of parabolic equations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 147, pp. 124–137, 1985.The authors are grateful to S. V. Kislyakov, whose remarks have allowed us to extend the class of the considered operators T, and to E. M. Dyn'kin for bibliographical information.     

变量核分数次积分在Hardy空间的有界性

§ 1　 Introduction and main resultsLet Sn- 1 be the unitsphere in Rn(n≥ 2 ) equipped with normalized Lebesgue measure dσ= dσ(z′) .We say that a functionΩ(x,z) defined on Rn× Rnbelongs to L∞ (Rn)× Lr(Sn- 1 )(r≥ 1 ) ,ifΩ(x,z) satisfies the following two conditions,(i) for any x,z∈Rnandλ>0 ,there hasΩ(x,λz) =Ω(x,z) ;(ii)‖Ω‖L∞(Rn)× Lr(Sn- 1) :=supx∈ Rn∫Sn- 1|Ω(x,z′) | rdσ(z′) 1 / r<∞ .For 0 <α相似文献   

Commutators of Multilinear Singular Integrals with Lipschitz Functions

The boundedness of commutators of multilinear singular integrals with Lipschitz functions in product Lebesgue spaces is obtained.     

On multilinear oscillatory singular integrals with rough kernels

In this paper, for the multilinear oscillatory singular integral operators T_A defined by

     

Bergman kernels and local holomorphic Morse inequalities

Let (X,) be a hermitian manifold and let L^k be a high power of a hermitian holomorphic line bundle over X. Local versions of Demaillys holomorphic Morse inequalities (that give bounds on the dimension of the Dolbeault cohomology groups associated to L^k), are presented - after integration they give the usual holomorphic Morse inequalities. The local weak inequalities hold on any hermitian manifold (X,), regardless of compactness and completeness. The proofs, which are elementary, are based on a new approach to pointwise Bergman kernel estimates, where the kernels are estimated by a model kernel in Mathematics Subject Classification (2000): 32A25, 32L10, 32L20in final form: 19 June 2003