Conjugate kernels and convergence of harmonic singular integrals

L Bounds for Singular Integrals and Maximal Singular Integrals with Rough Kernels

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).

Harmonic Singular Integrals and Steerable Wavelets in L2(R)

Here we present a method of constructing steerable wavelet frames in L2(R) that generalizes and unifies previous approaches, including Simoncelli’s pyramid and Riesz wavelets. The motivation for steerable wavelets is the need to more accurately account for the orientation of data. Such wavelets can be constructed by decomposing an isotropic mother wavelet into a finite collection of oriented mo...

Harmonic singular integrals and steerable wavelets in L2(Rd)

Article history: Received 20 July 2012 Received in revised form 22 January 2013 Accepted 29 March 2013 Available online 6 April 2013 Communicated by Pierre G. Lemarié-Rieusset

Singular Integrals

In this paper I will a t tempt to describe the subject as it has developed in the last fifteen years, outlining the methods by which its problems have been approached and discussing its connections with other branches of Analysis. I t will perhaps be best to start by considering certain classical situations which lead naturally to singular integrals and which contain the seeds of some of the me...

Evaluating Singular and Nearly Singular Integrals Numerically