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About 3,271 papers for “singular integrals”

Singular Integrals

S. R. S. Varadhan · Courant lecture notes in mathematics · 2022

Cited by 0

Singular integrals /

Morley, Vivienne Esta, author., University of Chicago., United States. Air Force. Office of Scientific Research. · The Journal of the Abraham Lincoln Association

Cited by 0Open access

Singular integrals

Calderón, A. P. · Project Euclid (Cornell University) · 1966

Cited by 0

On commutators of singular integrals and bilinear singular integrals

Ronald R. Coifman, Yves Meyer · Transactions of the American Mathematical Society · 1975

Lp estimates for multilinear singular integrals generalizing Caldern's commutator integral are obtained.The methods introduced involve Fourier and Mellin analysis.1.In this paper we introduce new methods to obtain estimates for commutators of singular integrals as well as other related operators.Let A(f) = A(x)f(x) and H(f) = pvff(t)dt/(x -t).It has been shown byCaldern's theorem was proved using a characterization of the Hardy space HX(R) in terms of the Lusin area function.It is the special form of the kernel which permits analysis using complex variables.It will be shown here that these V estimates (as well as others) can also be obtained by making use of the Fourier transform followed by the Mellin transform.These ideas are applied to obtain estimates of the following typewhere l/r -l/px + l/p2 + l/p3, 1 < px < , 1 < p2 < , 1 < p3 < .Actually, results improving both (1.1) (1.2) can be obtained.In fact let a" h r\M -" f"y)dy, J- (x-y)3 where a = dA/dx, b = dB/dx.Then for > p > 0 we have (1.3) f\C(a, b, f) (x)\p dx < Cp f(a*(x)b*(x)f*(x)f dx, where a* is the Hardy-Littlewood maximal function of a.

Cited by 503Open access

On singular integrals

B. Bajšanski, R. Coifman · Proceedings of symposia in pure mathematics · 1967

Cited by 21

Multilinear singular integrals

Christoph Thiele · Publicacions Matemàtiques · 2002

We survey the thoery of multilinear singular integral operators with modulation symmetry. The basic example for this theory is the bilinear Hilbert transform and its multilinear variants. We outline a proof of boundedness of Carleson's operator which shows the close connection of this operator to multilinear singular integrals. We discuss particular multilinear singular integrals which historically arose in the study of eigenfunctions of Schrödinger operators.

Cited by 6Open access

Maximal Singular Integrals

Varopoulos Nicolas · ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE · 2009

We prove the L p boundedness of the maximal operators attached to the singular kernels introduced in [1]. These kernels are obtained by multiplying (pointwise) a classical convolution Calderon-Zygmund kernel with the perturbing factor [a] x,y (cf. below). The importance of these perturbations lies in potential theoretic applications (cf. [3, 7]).

Cited by 0Open access

Multilinear singular integrals

Thiele, C. M. · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · 2002

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L p bounds for singular integrals and maximal singular integrals

Loukas Grafakos, Atanas Stefanov · 1998

Abstract. Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x | n are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map Lp → Lp for 1 &amp;lt; p &amp;lt; ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H 1 (S n−1).

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