### scholarly work

Multiparameter Riesz Commutators, with M. Lacey, S. Petermichl and B. Wick, to appear Amer. J. Math.

An Introduction to Mathematical Cryptography, with J. Hoffstein, J. Silverman, Series: Undergraduate Textbooks in Mathematics, July 2008, Springer.

BMO from dyadic BMO on the bidisc, with Lesley Ward ,J. London Math. Soc. Vol 77 (2), April 2008, p. 524-544.

The L^p Dirichlet problem for second order elliptic equations and a p-adapted square function, with M. Dindos and S. Petermichl, J. Funct. Anal., Vol. 249, issue 2, 2007, p. 372-392.

Multiparameter paraproducts, with C. Muscalu, T. Tao, C. Thiele, Revista M. Ibero. Vol. 22, Number 3, 2006, p. 963-976.

Variations on the theme of Journe's lemma, with C. Cabrillo, M. Lacey, U. Molter, JourneLemma.pdf to appear, Houston J. Math.

On Estimating the Lattice Security of NTRU, with N. Howgrave-Graham, J. Hoffstein, W. Whyte, NTRULattice-2005-1.pdf

A covering lemma for rectangles in $\R^n$, with R. Fefferman, Proc. AMS.133 No. 11, p.3235-3241

A short proof of the Coifman-Meyer paraproduct theorem, , with C. Muscalu, T. Tao, C. Thiele, C-M.pdf

Biparameter paraproducts, with C. Muscalu, T. Tao, C. Thiele, biparam.pdf , Acta Mathematica 193 (2004) , p.269-296.

NTRUSign: Digital signatures using the NTRU lattice, with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte, Proceedings of CT-RSA 2003, NTRUSign.pdf

Lectures at the L'Institut Fourier 2002 Summer School in Cryptology on NTRU encryption and digital signatures, grenoble.pdf

NTRUSign: Digital signatures using the NTRU lattice, extended version, with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte,2002 , NTRUSignextended.pdf

The Dirichlet problem for elliptic equations with drift terms, with C. Kenig, Publicaciones Matematiques 45 (2001), 199-217 Dir.dvi

NSS: An NTRU lattice-based signature scheme, with J. Hoffstein and J. Silverman, Proceedings of Eurocrypt 2001.

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

The absolute continuity of elliptic measure revisited. J. Fourier Anal. Appl. 4 (1998), no. 4-5, 463--468. w/Kenig, Carlos E.

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

Multiparameter operators and sharp weighted inequalities. Amer. J. Math. 119 (1997), no. 2, 337--369. w/Fefferman, R.

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.

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;

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

Maximum principles for the polyharmonic equation on Lipschitz domains. Potential Anal. 4 (1995), no. 6, 615--636. w/Verchota, G. C.

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.

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

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.

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 Neumann problem for elliptic equations with nonsmooth coefficients. Invent. Math. 113 (1993), no. 3, 447--509. w/Kenig, Carlos E.

A martingale inequality related to exponential square integrability. Proc. Amer. Math. Soc. 118 (1993), no. 2, 541--546.

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

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.

Area integral estimates for the biharmonic operator in Lipschitz domains. Trans. Amer. Math. Soc. 327 (1991), no. 2, 903--917. w/Verchota, Gregory

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

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.

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.

Oblique derivative problems for the Laplacian in Lipschitz domains. Rev. Mat. Iberoamericana 3 (1987), no. 3-4, 455--472.

Hardy spaces and the Dirichlet problem on Lipschitz domains. Rev. Mat. Iberoamericana 3 (1987), no. 2, 191--247. w/Kenig, Carlos E.

Journé's covering lemma and its extension to higher dimensions. Duke Math. J. 53 (1986), no. 3, 683--690.

Bounded double square functions. Ann. Inst. Fourier (Grenoble) 36 (1986), no. 2, 69--82.