Non-homogeneous strongly singular integrals

Gauss-chebyshev Quadrature Formulae for Strongly Singular Integrals

This paper presents some explicit results concerning an extension of the mechanical quadrature technique, namely, the Gauss-Jacobi numerical integration scheme, to the class of integrals whose kernels exhibit second order of singularity (i.e., one degree more singular than Cauchy). In order to ascribe numerical values to these integrals they must be understood in Hadamard's finite-part sense. T...

Strongly singular integrals along curves on α-modulation spaces

In this paper, we study the strongly singular integrals [Formula: see text] along homogeneous curves [Formula: see text]. We prove that [Formula: see text] is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces.

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...

Multi-parameter singular integrals

Evaluating Singular and Nearly Singular Integrals Numerically