Professor Department of Mathematics American University of Beirut

 

Office	310 Bliss
Phone	4233
E-mail	bshayya (at) aub (dot) edu (dot) lb
Photo	B. Shayya
Mailing Address	American University of Beirut P.O. Box 11-0236 / Mathematics Riad El-Solh / Beirut 1107 2020 Lebanon
Office Hours	11:00 – 11:50 MWF

 

Teaching

• Fall 2024: Calculus and Analytic Geometry III (Math 201)
• All semesters

Research

Research area: Harmonic analysis

Articles published or submitted:

• A family of fractal Fourier restriction estimates with implications on the Kakeya problem, Journal of Fourier Analysis and Applications, 30 (2024), no. 1, Paper No. 8, 33 pp; doi:10.1007/s00041-023-10065-9.
  Preprint available at arXiv:2206.12971.
• Mizohata-Takeuchi estimates in the plane, Bulletin of the London Mathematical Society, 55 (2023), no. 5, 2176–2194; doi:10.1112/blms.12843.
  Preprint available at arXiv:2208.10305.
• Improved weighted restriction estimates in R^3, Journal of Geometric Analysis, 33 (2023), no. 9, Paper No. 294, 25 pp; doi:10.1007/s12220-023-01364-0.
  Preprint available at arXiv:2206.06325.
• Fourier restriction in low fractal dimensions, Proceedings of the Edinburgh Mathematical Society, 64 (2021), no. 2, 373–407; doi:10.1017/S0013091521000201.
  Preprint available at arXiv:1905.09513.
• Weighted restriction estimates using polynomial partitioning, Proceedings of the London Mathematical Society, 115 (2017), no. 3, 545–598; doi:10.1112/plms.12046.
  Preprint available at arXiv:1512.03238.
• Variants of the Mattila integral, measures with nonnegative Fourier transforms, and the distance set problem, Transactions of the American Mathematical Society, 368 (2016), no. 4, 2623–2644.
  Preprint available here.
• When the cone in Bochner’s theorem has an opening less than {pi}, Bulletin of the London Mathematical Society, 44 (2012), no. 2, 207–221; doi:10.1112/blms/bdr087.
• The WAT conjecture on the torus, Proceedings of the American Mathematical Society, 139 (2011), no. 10, 3633–3643.
• Measures with Fourier transforms in L^2 of a half-space, Canadian Mathematical Bulletin, 54 (2011), no. 1, 172–179.
• Affine restriction for radial surfaces, Mathematische Zeitschrift, 262 (2009), no. 1, 41–55.
• Non-homogeneous strongly singular integrals, Studia Mathematica, 187 (2008), no. 3, 265–280.
• An affine restriction estimate in R^3, Proceedings of the American Mathematical Society, 135 (2007), no. 4, 1107–1113.
• Fourier restriction to convex surfaces of revolution in R^3 (with F. Abi-Khuzam), Publicacions Matemàtiques, 50 (2006), 71–85.
• Spherical means associated with non-isotropic dilation groups (with F. Abi-Khuzam), Results in Mathematics, 45 (2004), 195–200.
• Adjoint restriction estimates and scaling on spheres, Proceedings of the American Mathematical Society, 132 (2004), no. 5, 1517–1524.
• A class of non-homogeneous singular integrals in R^n (with F. Abi-Khuzam), Journal of Mathematical Analysis and Applications, 288 (2003), 274–284.
• Nonisotropic strongly singular integral operators, Transactions of the American Mathematical Society, 354 (2002), no. 12, 4893–4907.
• A sharp norm inequality for non-isotropic distance functions on R^n (with F. Abi-Khuzam), Mathematical Inequalities and Applications, 5 (2002), no. 3, 361–368.
• Singular integrals with nonhomogeneous oscillatory kernels, Indiana University Math Journal 50 (2001), no. 2, 1015–1025.
• On a singular integral estimate for the maximum modulus of a canonical product (with F. Abi-Khuzam), Illinois Journal of Math 44 (2000), no. 3, 551–555.

Preprints:

• A remark on the WAT conjecture (with F. Abi-Khuzam), preprint, 2009. pdf