We study the Marcinkiewicz integral operator M f(x) = ( ∫∞ −∞ | ∫ |y|≤2t f (x − (y))(Ω(y)/|y|n−1)dy|2dt/22t)1/2, where is a polynomial mapping from Rn into Rd and Ω is a homogeneous function of degree zero on Rn with mean value zero over the unit sphere Sn−1. We prove an Lp boundedness result of M for rough Ω. 2000 Mathematics Subject Classification. 42B20, 42B15, 42B25.

This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Dau...

In this paper we show how the properties of integral operators and their approximations are reeected in the performance of the GMRES iteration and how these properties can be used to smooth the GMRES iterates, thereby strengthening the norm in which convergence takes place. The smoothed iteration has very similar properties to Broyden's method and we present some comparisons of the two methods ...

We study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and Meyer via the introduction of an oscillatory factor containing a real-valued phase of five variables Φ(x, y1, y2, ξ1, ξ2) which is jointly homogeneous in the phase variables (ξ1, ξ2). For symbols of or...