Eric T. Sawyer

Mailing Address:

HH 311A
Department of Mathematics and Statistics
McMaster
University
1280 Main Street West
Hamilton, ON L8S 4K1

Phone:

(905) 525-9140 x 23407

 

 

Fax:

(905) 522-0935

 

 

Email:

sawyer@mcmaster.ca

 

Short Description of Research 2005-2009

 

Links to Papers, Books and Lecture Notes

 

Papers

 

E. Sawyer, An expanded version of `A two weight inequality for the Hilbert transform: a real variable characterization http://arxiv.org/abs/1201.4319’. In this paper we give a proof with expanded details, and additional background, of the real variable characterization of the two weight inequality for the Hilbert transform given in http://arxiv.org/abs/1201.4319 by M. L. Lacey, E. T. Sawyer, C.-Y. Shen and I. Uriarte-Tuero. There is also a slight reorganization of the proof. All of the arguments are due to Lacey, Sawyer, Shen and Uriarte-Tuero, but any errors, omissions and/or confusion introduced into this expanded version are due to this author alone. Here is the most recent version: http://www.math.mcmaster.ca/~sawyer/Publications/IndicatorCharacterizationExpanded3.pdf

 

M. Lacey, E. Sawyer, and I. Uriarte-Tuero, Astala's conjecture on distortion of Hausdorff measure under quasiconformal maps, to appear in Acta. Math. http://arxiv.org/abs/0805.4711

 

M. Lacey, E. Sawyer, and I. Uriarte-Tuero, A characterization of two weight norm inequalities for maximal singular integrals. http://arxiv.org/abs/0807.0246

 

M. Lacey, E. Sawyer, and I. Uriarte-Tuero, Two Weight Inequalities for Maximal Truncations of Dyadic Calderón-Zygmund Operators. http://arxiv.org/abs/0911.3920

 

M. Lacey, E. Sawyer, and I. Uriarte-Tuero, Two Weight Inequalities for Discrete Positive Operators. http://arxiv.org/abs/0911.3437

 

S. Costea, E.Sawyer and B. Wick, The corona theorem for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on the unit ball in Cⁿ. http://arxiv.org/abs/0811.0627

 

S. Costea, E.Sawyer and B. Wick, BMO estimates for the H^{}(B_{n}) corona problem. http://arxiv.org/abs/0905.1476

 

Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric and B. Wick, Bilinear forms on the Dirichlet space, to appear in Analysis and PDE. http://arxiv.org/abs/0811.4107

 

Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric, Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls, Adv. Math. 218 (2008), no. 4, 1107--1180. http://arxiv.org/abs/0706.0435

 

Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric, Carleson measures and interpolating sequences for Besov spaces on complex balls, Mem. Amer. Math. Soc. 182 (2006) no. 859, vi+163 pp. early version: http://www.math.mcmaster.ca/~sawyer/Publications/ars17jan.pdf

 

Rios, Cristian; Sawyer, Eric T.; Wheeden, Richard L., Regularity of subelliptic Monge-Ampère equations, Adv. Math. 217 (2008), no. 3, 967-1026. early version: http://www.math.mcmaster.ca/~sawyer/Publications/part4auglegendre.pdf

 

Guan, Pengfei; Sawyer, Eric, Regularity of subelliptic Monge-Ampère equations in the plane, Trans. Amer. Math. Soc. 361 (2009), no. 9, 4581--4591. early version: . http://www.math.mcmaster.ca/~sawyer/Publications/Gu_Saw_Mean-9-7-2007.pdf

 

Rios, C. and Sawyer, E., Smoothness of radial solutions to the Monge-Ampère equation, Proc. Amer. Math. Soc. 137 (2009), no. 4, 1373--1379. http://arxiv.org/abs/0804.2497

 

Sawyer, Eric T.; Wheeden, Richard L., Hölder continuity of weak solutions to subelliptic equations with rough coefficients, Mem. Amer. Math. Soc. 180 (2006) no. 847, x+157 pp. early version:  http://www.math.mcmaster.ca/~sawyer/Publications/swmemoirsrev.pdf

 

Sawyer, Eric T.; Wheeden, Richard L., Degenerate Sobolev spaces and regularity of subelliptic equations, Trans. A. M. S., article electronically published on October 30, 2009. early version: http:/www.math.mcmaster.ca/~sawyer/Publications/DegenerateSob24revfix3.pdf

 

Sawyer, Eric T.; Wheeden, Richard L., Regularity of degenerate Monge-Ampère and prescribed Gaussian curvature equations in two dimensions, Potential Anal. 24 (2006), no. 3 267-301. early version: http:/www.math.mcmaster.ca/~sawyer/Publications/amperei.pdf

 

Sawyer, Eric T.; Wheeden, Richard L., A priori estimates for quasilinear equations related to the Monge-Ampère equation in two dimensions, J. Anal. Math. 97 (2005), 257-316. early version: http:/www.math.mcmaster.ca/~sawyer/Publications/apriori.pdf

 

Rios, Cristian; Sawyer, Eric T.; Wheeden, Richard L., A higher-dimensional partial Legendre transform, and regularity of degenerate Monge-Ampère equations, Adv. Math. 193 (2005) no. 2, 373-415. early version: http://www.math.mcmaster.ca/~sawyer/Publications/part4auglegendre.pdf

 

Arcozzi, N.; Rochberg, R.; Sawyer, E., Some problems on Carleson measures for Besov-Sobolev spaces, Topics in complex analysis and operator theory, 141--148, Univ. Málaga, Málaga, 2007.

 

Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric, The characterization of the Carleson measures for analytic Besov spaces: a simple proof, Complex and harmonic analysis, 167--177, DEStech Publ., Inc., Lancaster, PA, 2007. http://arxiv.org/abs/0706.1936

 

Arcozzi, Nicola; Rochberg, Richard; Sawyer, Eric, The diameter space, a restriction of the Drury-Arveson-Hardy space, Function spaces 21-42, Contemp. Math., 435 (2007), Amer. Math. Soc., Providence, RI.

 

Iosevich, Alexander; Sawyer, Eric T.; Seeger, Andreas, Mean lattice point discrepancy bounds. II. Convex domains in the plane, J. Anal. Math. 101 (2007), 25-63. http://arxiv.org/abs/math/0501113

 

 

Books

 

Sawyer, E., Function Theory: Interpolation and Corona problems, Fields Institute Monograph series 25, American Math. Soc. 2009, ix + 203 pages.

 

 

Lecture Notes

 

Sawyer, Eric, Lecture Notes in Advanced Real Analysis 2010

 

Sawyer, Eric, Lecture Notes in Real Analysis 2009

 

Sawyer, Eric, Lecture Notes in Complex Analysis 2009

 

Sawyer, Eric, Functional Analysis and Applications 2006

 

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