M. Greenblatt

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math.CA2026

Fourier decay and $L^{p}$ Sobolev smoothing for weighted hypersurface measures in $R^{3}$

Michael Greenblatt

We consider local hypersurface measures in $R^{3}$ whose density is allowed to have a weight function constructed from real analytic functions in a broad sense. We prove $L…

math.CA2024

Oscillatory integrals and weighted gradient flows

Michael Greenblatt

We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on $(x_{1} \partial_{x_{1}} f (x), ..., x_{n} \partial_{x_{n}} f (x))$ , where $f (x)$ is the…

math.CA2024

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…

math.CA2024

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…

math.CA2024

Hessian determinants and averaging operators over surfaces in $R^{3}$

Michael Greenblatt

We prove $L^{p} (R^{3})$ to $L_{s}^{p} (R^{3})$ Sobolev improvement theorems for local averaging operators over real analytic surfaces in $R^{3}$ . For most such ope…

Fourier decay and Lp Sobolev smoothing for weighted hypersurface measures in R3

Oscillatory integrals and weighted gradient flows

Convexity, Fourier transforms, and lattice point discrepancy

A method for bounding oscillatory integrals in terms of non-oscillatory integrals

Hessian determinants and averaging operators over surfaces in R3

Fourier decay and $L^{p}$ Sobolev smoothing for weighted hypersurface measures in $R^{3}$

Hessian determinants and averaging operators over surfaces in $R^{3}$