8 citations · 14 across the 23 of their papers we have counts for
29 papers
Fourier decay and Sobolev smoothing for weighted hypersurface measures in
Michael Greenblatt
We consider local hypersurface measures in whose density is allowed to have a weight function constructed from real analytic functions in a broad sense. We prove $L…
Oscillatory integrals and weighted gradient flows
Michael Greenblatt
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on , where is the…
Convexity, Fourier transforms, and lattice point discrepancy
Michael Greenblatt
In a well-known paper by Bruna, Nagel and Wainger [BNW], Fourier transform decay estimates were proved for smooth hypersurfaces of finite line type bounding a convex domain. In thi…
A method for bounding oscillatory integrals in terms of non-oscillatory integrals
Michael Greenblatt
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an app…
Hessian determinants and averaging operators over surfaces in
Michael Greenblatt
We prove to Sobolev improvement theorems for local averaging operators over real analytic surfaces in . For most such ope…
Hyperplane integrability conditions and smoothing for Radon transforms
Michael Greenblatt
This paper may be viewed as a companion paper to [G1]. In that paper, Sobolev estimates derived from a Newton polyhedron-based resolution of singularities method are combined…