Papers
This page is no longer being maintained. You will find my most recent papers by searching for my name at https://arxiv.org/archive/math or https://eprint.iacr.org/ |
Papers in .pdf format.
Square functions and the A_infinity property of elliptic measure with C. Kenig, B. Kirchheim, and T. Toro, http://arxiv.org/abs/1409.7131
Carleson measures and elliptic boundary value problems Proceedings of ICM 2014, CarlesonMeasure.pdf
Practical Signatures from the Partial Fourier Recovery Problem, with J. Hoffstein, j. Schanck, J. Silverman and W. Whyte, http://eprint.iacr.org/2013/757
Dyadic structure theorems for multiparameter function spaces, with J. Li and L. Ward, to appear in Revista IberoAmer. LiPipherWard_RMI_2013.pdf
The Regularity problem for second order elliptic operators with complex-valued non-smooth coefficients, with S. Hofmann, C. Kenig, S. Mayboroda, to appear Mat. Annalen, preprint available at http://arxiv.org/abs/1301.5209 .
Diophantine Approximation and directional discrepancy of rotated lattices, with D. Bilyk, X. Ma, and C. Spencer, bmps29.pdf to appear in TAMS,
Perturbations of elliptic operators with E. Milakis, T. Toro, to appear in Harmonic Analysis and Partial Differential Equations, Contemporary Mathematics, vol. 612, Amer. Math. Soc.,143-161 http://arxiv.org/abs/1210.5591
Boundary value problems for second order elliptic operators satisfying a Carleson condition, with M. Dindos, D. Rule, preprint available at http://arxiv.org/abs/1301.0426
Square function/non-tangential maximal function estimates and the dirichlet problem for non-symmetric elliptic operators
with Steve Hofmann, Carlos Kenig, Svitlana Mayboroda, to appear in JAMS http://arxiv.org/abs/1202.2405
.
Harmonic analysis on chord-arc domains
with E. Milakis, T. Toro, J. Geometric Analysis, (2013), 23, 2091-2157 http://arxiv.org/abs/1101.0331
.
Practical Lattice-based Cryptography: NTRUEncrypt and NTRUSign
with J. Hoffstein, N. Howgrave-Graham, W. Whyte, in
The LLL Algorithm: Survey and Applications, Springer, 2010.
Multiparameter div-curl lemmas
with M. Lacey, S. Petermichl, B. Wick, Bull. London Math. Soc. (2012)
mpdivcurl.pdf
Directional discrepancy in two dimensions
with D. Bilyk, X. Ma, and C. Spencer,
Bulletin London Math. Soc. (2011), 43 (6), 1151-1166,
bmpsLMS.pdf
Geometric-arithmetic averaging of dyadic weights
with L. Ward and X. Xiao,
PWX2009.pdf
to appear Rev. Mat. Iberoamericana.
Weak-star convergence in multiparameter Hardy spaces,
with S. Treil, Proc. Amer. Math. Soc. 139 (2011), 1445-1454, available on Arxiv
here
BMO solvability and the A^infinity condition for
elliptic operators,
with M. Dindos, C. Kenig
bmoJul29.pdf, J. Geometric Analysis (2011), 21, 78-95
Iterated Riesz Commutators: a simple proof of boundedness,
with M. Lacey, S. Petermichl, B. Wick,
RieszUpperBound.pdf
Proceedings of Analysis at El Escorial, 2008.
Book:An Introduction to Mathematical Cryptography
with J. Hoffstein, J. Silverman, Series: Undergraduate
Textbooks in Mathematics, Springer, July 2008.
Multiparameter Riesz Commutators,
with M. Lacey, S. Petermichl, and B. Wick,
multiParameterRieszComm.pdf,, Amer. J. Math, Vol. 131, No.3,
(2009) p. 731-771.
The L^p Dirichlet problem for second order elliptic
operators and a p-adapted square function,
with M. Dindos and S. Petermichl
psqFinal.pdf , J. Funct. Anal. Vol. 249 issue 2, 2007, p. 372-392
BMO from dyadic BMO on the bidisc,
with Lesley Ward
BMOdyadicBMObidisc.pdf J. London Math. Soc. Vol. 77, Number 2 (2008), p. 524-544.
On Estimating the Lattice Security of NTRU,
with N. Howgrave-Graham, J. Hoffstein, W. Whyte,
NTRULattice-2005-1.pdf
Variations on the theme of Journe's lemma,
with C. Cabrillo, M. Lacey, U. Molter,
JourneLemma.pdf Houston J. Math., Vol 32, No. 3 (2006), p. 833.
Multiparameter paraproducts,
with C. Muscalu, T. Tao, C. Thiele, preprint,
polydisc.pdf
Revista M. Ibero. Vol. 22, Number 3, 2006, p. 963-976.
Biparameter paraproducts,
with C. Muscalu, T. Tao, C. Thiele,
biparam.pdf ,
Acta Mathematica, 193, (2004), p. 269-296
A short proof of the Coifman-Meyer paraproduct theorem,
with C. Muscalu, T. Tao, C. Thiele,
C-M.pdf
A covering lemma for rectangles in $\R^n$,
with R. Fefferman, 133 No. 11 (2005), p.3235-3241. Proc. AMS.,
coveringlemma.pdf
NTRUSign: Digital signatures using the NTRU lattice,
with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte,
Proceedings of CT-RSA 2003,
NTRUSign.pdf
NTRUSign: Digital signatures using the NTRU lattice,
extended version,
with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte, 2002,
NTRUSignextended.pdf
Lectures at the L'Institut Fourier 2002 Summer
School in Cryptology on NTRU encryption and digital signatures,
grenoble.pdf
NSS: An NTRU lattice-based signature scheme,
with J. Hoffstein and J. Silverman, Proceedings of Eurocrypt 2001.
The Dirichlet problem for elliptic equations with drift
terms,
with C. Kenig, Publicaciones Matematiques 45 (2001), 199-217
Dir.dvi
A new approach to absolute continuity of elliptic measure,
with applications to non-symmetric equations.
Adv. Math. 153 (2000)
, no. 2, 231--298. w/Kenig, C.; Koch, H.; Toro, T.
AbsoluteContinuity.pdf
NTRU: a ring-based public key cryptosystem.
Algorithmic number theory (Portland, OR, 1998), 267--288,
Lecture Notes in Comput. Sci., 1423
, Springer, Berlin, 1998.
w/Hoffstein, Jeffrey; Silverman, Joseph H.
The inhomogeneous Dirichlet problem for $\Delta\sp 2$
in Lipschitz domains.
J. Funct. Anal. 159 (1998),
no. 1, 137--190. w/Adolfsson, Vilhelm
The absolute continuity of elliptic measure revisited.
J. Fourier Anal. Appl. 4 (1998)
, no. 4-5, 463--468. w/Kenig, Carlos E.
Vector potential theory on nonsmooth domains in ${R}\sp
3$ and applications to electromagnetic scattering.
J. Fourier Anal. Appl. 3 (1997)
, no. 2, 131--192. w/Mitrea, Dorina; Mitrea, Marius;
Area integral estimates for higher order elliptic equations
and systems.
Ann. Inst. Fourier (Grenoble) 47 (1997)
, no. 5, 1425--1461.
w/Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
Littlewood-Paley estimates: some applications to elliptic
boundary value problems.
Partial differential equations
and their applications (Toronto, ON, 1995), 221--238,
CRM Proc. Lecture Notes, 12
, Amer. Math. Soc., Providence, RI, 1997.
fieldsinst.dvi
Multiparameter operators and sharp weighted inequalities.
Amer. J. Math. 119 (1997)
, no. 2, 337--369. w/Fefferman, R.
Review of: Harmonic Analysis Techniques in Second Order
Elliptic PDE, by Carlos Kenig, Bulletin of the AMS 33 (2) (1996), p.
229-236,
review.pdf
The Neumann problem for elliptic equations with nonsmooth
coefficients. II.
A celebration of John F. Nash, Jr.
Duke Math. J. 81 (1995)
, no. 1, 227--250 (1996).
w/Kenig, Carlos E.
Boundary value problems for higher order operators in
Lipschitz and $C\sp 1$ domains.
Fourier analysis and partial differential equations (Miraflores de la Sierra, 1992)
, 297--309, Stud. Adv. Math., CRC, Boca Raton, FL, 1995.
Maximum principles for the polyharmonic equation on Lipschitz
domains.
Potential Anal. 4 (1995)
, no. 6, 615--636.
w/Verchota, G. C.
Dilation invariant estimates and the boundary Gårding
inequality for higher order elliptic operators.
Ann. of Math. (2) 142 (1995)
, no. 1, 1--38.
w/Verchota, Gregory C.
The Neumann problem for elliptic equations with nonsmooth
coefficients.
Invent. Math. 113 (1993)
, no. 3, 447--509. w/Kenig, Carlos E.
A maximum principle for biharmonic functions in Lipschitz
and $C\sp 1$ domains.
Comment. Math. Helv. 68 (1993)
, no. 3, 385--414. w/Verchota, G.
The Dirichlet problem in $L\sp p$ for the biharmonic
equation on Lipschitz domains.
Amer. J. Math. 114 (1992)
, no. 5, 923--972. w/Verchota, Gregory
A martingale inequality related to exponential square
integrability.
Proc. Amer. Math. Soc. 118 (1993)
, no. 2, 541--546.
The theory of weights and the Dirichlet problem for elliptic
equations.
Ann. of Math. (2) 134 (1991)
, no. 1, 65--124. w/Fefferman, R. A.; Kenig, C. E.
Partial differential equations with minimal smoothness
and applications.
Proceedings of the IMA Participating
Institutions Conference held at the University of Chicago
, Chicago, Illinois, March 21--25, 1990. Edited by B. Dahlberg,
E. Fabes, R. Fefferman, D. Jerison, C. Kenig and J. Pipher. The
IMA Volumes in Mathematics and its Applications, 42. Springer-Verlag,
New York, 1992. xii+220 pp. ISBN: 0-387-97774-0
Area integral estimates for the biharmonic operator in
Lipschitz domains.
Trans. Amer. Math. Soc. 327 (1991)
, no. 2, 903--917. w/Verchota, Gregory
The $h$-path distribution of the lifetime of conditioned
Brownian motion for nonsmooth domains.
Probab. Theory Related Fields 82 (1989)
, no. 4, 615--623. w/Kenig, Carlos E.
Hardy spaces and the Dirichlet problem on Lipschitz domains.
Rev. Mat. Iberoamericana 3 (1987)
, no. 2, 191--247. w/Kenig, Carlos E.
Oblique derivative problems for the Laplacian in Lipschitz
domains.
Rev. Mat. Iberoamericana 3 (1987)
, no. 3-4, 455--472.
The oblique derivative problem on Lipschitz domains with
$L\sp p$ data.
Amer. J. Math. 110 (1988)
, no. 4, 715--737. w/Kenig, Carlos E.
Bounded double square functions.
Ann. Inst. Fourier (Grenoble) 36 (1986)
, no. 2, 69--82.
Journé's covering lemma and its extension to higher
dimensions.
Duke Math. J. 53 (1986)
, no. 3, 683--690.