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pro vyhledávání: '"Greenblatt, Michael"'
Autor:
Greenblatt, Michael
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 phase function. We prove a theorem which provides estimates that are u
Externí odkaz:
http://arxiv.org/abs/2403.12751
Autor:
Greenblatt, Michael
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 this paper, we generalize their results in the following ways. First, for
Externí odkaz:
http://arxiv.org/abs/2402.16636
Autor:
Greenblatt, Michael
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 appropriate sense and behave well under perturbations of the phase. As a
Externí odkaz:
http://arxiv.org/abs/2210.09093
Autor:
Greenblatt, Michael
We prove $L^p({\mathbb R}^3)$ to $L^p_s({\mathbb R}^3)$ Sobolev improvement theorems for local averaging operators over real analytic surfaces in ${\mathbb R}^3$. For most such operators, in a sense made precise in the paper, the set of $(p,s)$ for w
Externí odkaz:
http://arxiv.org/abs/2112.01461
Autor:
Greenblatt, Michael
This paper may be viewed as a companion paper to [G1]. In that paper, $L^2$ Sobolev estimates derived from a Newton polyhedron-based resolution of singularities method are combined with interpolation arguments to prove $L^p$ to $L^q_s$ estimates, som
Externí odkaz:
http://arxiv.org/abs/1910.09107
Autor:
Greenblatt, Michael
We extend the theorems of [G1] on $L^p$ to $L^p_s$ Sobolev improvement for translation invariant Radon and fractional singular Radon transforms over hypersurfaces, proving $L^p$ to $L^q_s$ boundedness results for such operators. Here $q \geq p$ but $
Externí odkaz:
http://arxiv.org/abs/1910.04547
Fourier transforms of indicator functions, lattice point discrepancy, and the stability of integrals
Autor:
Greenblatt, Michael
We prove sharp estimates for Fourier transforms of indicator functions of bounded open sets in ${\mathbb R}^n$ with real analytic boundary, as well as nontrivial lattice point discrepancy results. Both will be derived from estimates on Fourier transf
Externí odkaz:
http://arxiv.org/abs/1810.10507
Autor:
Greenblatt, Michael
In the paper [G1] the author proved $L^p$ Sobolev regularity results for averaging operators over hypersurfaces and connected them to associated Newton polyhedra. In this paper, we use rather different resolution of singularities techniques to prove
Externí odkaz:
http://arxiv.org/abs/1803.09679
Autor:
Greenblatt, Michael
$L^p$ to $L^p_{\beta}$ boundedness theorems are proven for translation invariant averaging operators over hypersurfaces in Euclidean space. The operators can either be Radon transforms or averaging operators with multiparameter fractional integral ke
Externí odkaz:
http://arxiv.org/abs/1802.03814
Autor:
Greenblatt, Michael
We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta < 2$. Suppo
Externí odkaz:
http://arxiv.org/abs/1703.00637