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- J. Csima, Eric Sawyer
- Discrete & Computational Geometry
- 1993

In 1958 L. M. Kelly and W, O, J. Moser showed that apart from a pencil, any configuration of n lines in the real projective plane has at least 3n/7 ordinary or simple points of intersection, with equality in the Kelly-Moser example (a complete quadrilateral with its three diagonal lines). In 1981 S. Hansen claimed to have improved this to n/2 (apart from… (More)

- Nicola Arcozzi, Richard Rochberg, Eric Sawyer, Brett D. Wick
- J. London Math. Society
- 2011

- Cristian Ríos, Eric Sawyer, RICHARD L. WHEEDEN
- 2003

A!"#$%&#. In dimension n ≥ 3, we deÞne a generalization of the classical two dimensional partial Legendre transform, that reduces interior regularity of the generalized Monge-Ampère equation detD2u = k (x, u,Du) to regularity of a divergence form quasilinear system of special form. This is then used to obtain smoothness of C2,1 solutions, having n − 1… (More)

- Cristian Ríos, Eric Sawyer
- 2008

are smooth, given that k is smooth and nonnegative. When u is radial, (1) reduces to a nonlinear ODE on [0, 1) that is singular at the endpoint 0. It is thus easy to prove that u is always smooth away from the origin, even where k vanishes, but smoothness at the origin is more complicated, and determined by the order of vanishing of k there. In fact, Monn… (More)

- R. KERMAN, Eric Sawyer
- 2010

Let T be a positive linear operator defined for nonnegative functions on a rj-finite measure space {X,m,fi). Given 1 < p < oo and a nonnegative weight function w on X , it is shown that there exists a nonnegative weight function v , finite /¿-almost everywhere on X , such that (1) I \Tf)*wdfi< j fvd/i, for all/>0, J x J x tere exists <j> posi ( h if and… (More)

We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.

Let E ⊂ C be a compact set, g : C → C be a K-quasiconformal map, and let 0 < t < 2. Let H denote t-dimensional Hausdorff measure. Then H(E) = 0 =⇒ H ′ (gE) = 0 , t′ = 2Kt 2 + (K − 1)t . This is a refinement of a set of inequalities on the distortion of Hausdorff dimensions by quasiconformal maps proved by K. Astala [2] and answers in the positive a… (More)

- Pengfei Guan, Eric Sawyer
- 2009

We establish a C∞ regularity result for C1,1 solutions of degenerate Monge-Ampère equation in R2, under the assumption that the trace of the Hessian is bounded from below.

- Eric Sawyer, Carlos Pérez, Sheldy Ombrosi
- 2008

where to fix ideas, the operator T is either the Hardy-Littlewood maximal operator or any Calderón-Zygmund Operator. Versions of these type of inequalities were studied by Sawyer in [Sa] motivated by the work of Muckenhoupt and Wheeden [MW] (see also the works [AM] and [MOS]). E. Sawyer proved that inequality (1.1) holds in R when T = M is the… (More)

- José. A. Adell, Richard Rochberg, Eric Sawyer, Brett D. Wick, Rauno Aulaskari, Oscar Blasco
- 2010

We discuss the mth order Bergman metric and the mth order Carathéodory-Reiffen metric of Burbea, and a new higher order metric arised in the study of Berezin’s operator calculus on bounded domains in C. Some comparison results among them and the corresponding classical intrinsic metrics are established on certain domains. Inequalities for eigenvalues of… (More)