This paper applies a modern method of singularity resolution in algebraic geometry to resolving singularities of integral operators in Fourier analysis. This is achieved by introducing a method of mixed variables that is equivalent to changing coordinates for integral operators. We decompose the integral operator into dyadic pieces via monomial transforms and the mixed-variable method so as to obtain its sharp estimates on different domains. These sharp estimates can be written in an elegant form in terms of continued fractions.
Cite this article
Sheng-Ming Ma, Resolution of Operator Singularities via the Mixed-Variable Method. Publ. Res. Inst. Math. Sci. 45 (2009), no. 2, pp. 569–599DOI 10.2977/PRIMS/1241553130