Eric
T. Sawyer
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Mailing Address: |
HH
311A |
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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
M. Lacey, E. Sawyer, and
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
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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