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.     

Rough Marcinkiewicz integrals along certain smooth curves

This paper is devoted to the study of the multiple-parameter rough Marcinkiewicz integral operators associated with certain smooth curves. It is shown that the Grafakos-Stefanov type size condition F_α (S^m-1 × S^n-1) of the kernel implies the L^p-boundedness of these Marcinkiewicz integral operators for some α>1/2 and 1+12α<p<1+2α, which is an essential improvement of certain previous results.     

Classes of singular integrals along curves and surfaces

This paper is concerned with singular convolution operators in , , with convolution kernels supported on radial surfaces . We show that if , then boundedness holds if and only if . This statement can be reduced to a similar statement about the multiplier in . We also construct smooth for which the corresponding operators are bounded for but unbounded for , for given . Finally we discuss some examples of singular integrals along convex curves in the plane, with odd extensions.

     

Rough singular integrals and maximal operators with mixed homogeneity along compound curves

The parabolic singular integrals along certain compound curves as well as the related maximal operators are considered. Under rather weakened size conditions on the integral kernels both on the unit sphere and in the radial direction, the ‐mapping properties for such operators are established. Some previous results are greatly extended and improved.     

On Laplacian integrals with singular kernels

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

Singular integrals with exponential weights

We study the operators

where is the Hardy-Littlewood maximal function, the Hilbert transform or Carleson operator.

Under suitable conditions on the weight of exponential type, we prove boundedness of from spaces, defined on with respect to the measure to with the same density measure. These operators, that arise in questions of harmonic analysis on noncompact symmetric spaces, are bounded from to if and only if .

     

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   

Rough bilinear fractional integrals with variable kernels

We study the rough bilinear fractional integral

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.     

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.     

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.     

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.