258 citations · 1k across the 35 of their papers we have counts for
28 papers · 1 filter
Finiteness of the Hölder-Brascamp-Lieb Constant Revisited
Philip T. Gressman
Abstract Hölder-Brascamp-Lieb inequalities have become a ubiquitous tool in Fourier analysis in recent years, due in large part to a theorem of Bennett, Carbery, Christ, and Tao (2…
Generalized Sublevel Estimates for Form-Valued Functions and Related Results for Radon-like Transforms
Philip T. Gressman
Motivated by the testing condition for Radon-Brascamp-Lieb multilinear functionals established in arXiv:2201.12201, this paper is concerned with identifying local conditions on smo…
Local curvature of maximally nondegenerate Radon-like transforms
Philip T. Gressman
This paper gives a complete geometric characterization in all dimensions and codimensions of those Radon-like transforms which, up to endpoints, satisfy the largest possible range…
A new type of superorthogonality
Philip T. Gressman, Lillian B. Pierce, Joris Roos +1
We provide a simple criterion on a family of functions that implies a square function estimate on for every even integer . This defines a new type of superorthogona…
On frames of smooth, compactly-supported wave packets adapted to tilings of frequency space
Philip T. Gressman
We establish a broad notion of admissible tilings of frequency space which admit associated wave packet frames with elements which are smooth and compactly supported. The framework…
Testing conditions for multilinear Radon-Brascamp-Lieb inequalities
Philip T Gressman
This paper establishes a necessary and sufficient condition for -boundedness of a class of multilinear functionals which includes both the Brascamp-Lieb inequalities and gener…
On the strict majorant property in arbitrary dimensions
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2
In this work we study -dimensional majorant properties. We prove that a set of frequencies in satisfies the strict majorant property on for all $p…
-improving estimates for Radon-like operators and the Kakeya-Brascamp-Lieb inequality
Philip T. Gressman
This paper considers the problem of establishing -improving inequalities for Radon-like operators in intermediate dimensions (i.e., for averages overs submanifolds which are n…
Multilinear oscillatory integral operators and geometric stability
Philip T. Gressman, Ellen Urheim
In this article we prove a sharp decay estimate for certain multilinear oscillatory integral operators of a form inspired by the general framework of Christ, Li, Tao, and Thiele [6…
Reversing a philosophy: from counting to square functions and decoupling
Philip T. Gressman, Shaoming Guo, Lillian B. Pierce +2
Breakthrough work of Bourgain, Demeter, and Guth recently established that decoupling inequalities can prove powerful results on counting integral solutions to systems of Diophanti…
Geometric averaging operators and nonconcentration inequalities
Philip T Gressman
This paper is devoted to a systematic study of certain geometric integral inequalities which arise in continuum combinatorial approaches to -improving inequalities for Radon-l…
On the Oberlin affine curvature condition
Philip T. Gressman
In this paper we generalize the well-known notions of affine arclength and affine hypersurface measure to submanifolds of any dimension in , .…
Higher decay inequalities for multilinear oscillatory integrals
Maxim Gilula, Philip T. Gressman, Lechao Xiao
In this paper we establish sharp estimates (up to logarithmic losses) for the multilinear oscillatory integral operator studied by Phong, Stein, and Sturm and Carbery and Wright on…
Generalized curvature for certain Radon-like operators of intermediate dimension
Philip T. Gressman
This paper establishes -improving estimates for a variety of Radon-like transforms which integrate functions over submanifolds of intermediate dimension. In each case, the res…
Fourier extension for extremal quadratic submanifolds
Philip T. Gressman
This note establishes the full range of -- Fourier extension estimates for the model -dimensional quadratic submanifold in parametrized by $γ(…
Maximal Decay Inequalities for Trilinear oscillatory integrals of convolution type
Philip T. Gressman, Lechao Xiao
In this paper we prove sharp -- decay for certain trilinear oscillatory integral forms of convolution type on . These estimates imply ear…
On a trilinear singular integral form with determinantal kernel
Philip Gressman, Danqing He, Vjekoslav Kovač +3
We study a trilinear singular integral form acting on two-dimensional functions and possessing invariances under arbitrary matrix dilations and linear modulations. One part of the…
Damping oscillatory integrals by the Hessian determinant via Schrödinger
Philip T. Gressman
We consider the question of when it is possible to force a degenerate scalar oscillatory integral to decay as fast as a nondegenerate one by restricting the support to the region w…
-nondegenerate Radon-like operators with vanishing rotational curvature
Philip T. Gressman
We consider the mapping properties of a model family of Radon-like operators integrating functions over n-dimensional submanifolds of . It i…
An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems
Yen Do, Philip T. Gressman
We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of os…
Scalar oscillatory integrals in smooth spaces of homogeneous type
Philip T. Gressman
We consider a generalization of the notion of spaces of homogeneous type, inspired by recent work of Street [21] on the multi-parameter Carnot-Caratheodory geometry, which imbues s…
Fractional Poincare and logarithmic Sobolev inequalities for measure spaces
Philip T. Gressman
We prove generalizations of the Poincare and logarithmic Sobolev inequalities corresponding to the case of fractional derivatives in measure spaces with only a minimal amount of ge…
Uniform sublevel Radon-like inequalities
Philip T. Gressman
This paper is concerned with establishing uniform weighted - estimates for a class of operators generalizing both Radon-like operators and sublevel set operators. Such es…
On multilinear determinant functionals
Philip T. Gressman
This paper considers the problem of -estimates for a certain multilinear functional involving integration against a kernel with the structure of a determinant. Examples of suc…