Malabika Pramanik's Research
Areas of interest
- Euclidean harmonic analysis
- Cone multipliers and local smoothing
- Multi-parameter maximal functions
- Hilbert transform along polynomial surfaces
- Scalar oscillatory integrals, oscillatory integrals
with degenerate phases
- Almost everywhere convergence of Fourier series
- Multilinear operators with singular multipliers
- Several complex variables: Estimates for
the Bergman kernel.
- Partial differential equations
- Inverse problems and microlocal analysis
Background
I got my Ph.D. in Mathematics from the University of California, Berkeley, under the
guidance of Prof. Michael Christ. I was a Van Vleck visiting assistant
professor at University of Wisconsin, Madison (2001-2004),
visiting assistant professor at the University of Rochester (Fall
2004), and a Fairchild Senior Research Fellow at Caltech (January 2005 - August 2006). I joined the Mathematics Department at UBC in Fall 2006. (For more details, here is a copy of my CV in PDF format).
Publications
- A multi-dimensional resolution of singularities with applications to
analysis. (Joint work with Tristan Collins and Allan Greenleaf) To appear in Amer. J. Math. ArXiv preprint.
- Maximal operators and differentiation theorems for sparse sets. (Joint work with
Izabella Laba) To appear in Duke Math. J.
- An FIO calculus for marine seismic imaging, II: Sobolev estimates (Joint work with
Raluca Felea and Allan Greenleaf) Math. Annalen DOI: 10.1007/s00208-011-0644-5.
- A Calderón-Zygmund estimate with applications
to generalized Radon transforms and Fourier integral operators. (Joint work with
Keith Rogers and Andreas Seeger) Studia Math., 202 (2011), 1-15.
- Multilinear singular operators with fractional rank. (Joint work with
Ciprian Demeter and Christoph Thiele) Pacific J. of Mathematics 246 (2010) no. 2, 293--324
- Maximal averages over linear and monomial polyhedra. (Joint work
with Alexander Nagel) Duke Math. J. Volume 149 Number 2 (2009), 209-277.
- Arithmetic progressions in sets of fractional dimension. (Joint work with
Izabella Laba) Geom. Funct. Anal. 19 (2009), 429-456.
- Oscillatory integral operators with homogeneous
polynomial phases in several variables. (Joint work with
Allan Greenleaf and Wan Tang) J. Functional
Analysis (2007, volume 244, 444-487). (pdf)
- Double Hilbert transform
along real-analytic surfaces in $\mathbb{R}^{d+2}$.
(Joint work with Chan Woo Yang) J. London Math. Soc. (2008) 77(2):363-386.
- Averages over curves in
$\mathbb{R}^3$ and associated maximal functions.
(Joint work with Andreas Seeger) Amer. J. Math. (2007, volume 21, number 3, 61-103). (pdf)
- $L^p$ Sobolev regularity of a restricted X-ray
transform. (Joint work with Andreas Seeger) Harmonic Analysis and its Applications at Osaka, Conference
Proceedings (November 2004, 47-64). (pdf)
- Wolff's inequality for hypersurfaces. (Joint
work with Izabella Laba). To appear in the Proceedings of El
Escorial, 2005. (pdf)
- $L^p$ decay estimates for weighted oscillatory integral operator
on $\mathbb{R}$. (Joint work with Chan Woo Yang)
Revista Matematica Iberoamericana (2005, volume 21, number 3, 1071--1095). (pdf)
- Decay estimates for weighted scalar oscillatory integrals
on $\mathbb{R}^2$. (Joint work with Chan Woo Yang)
Indiana University Mathematical Journal (2004, volume 53,
number 2, 613-645).
(pdf)
- A weak $L^2$ estimate for a maximal dyadic sum operator on
$\mathbb{R}^n$. (Joint work with Erin Terwilleger) Illinois
Journal of Mathematics (2003, volume 47, number 3,
775-813). (pdf)
- Convergence of two-dimensional weighted integrals. Transactions
of the American Mathematical Society (2002, volume 354,
number 4, 1651-1665). (pdf)
- Weighted inequalities for real-analytic functions in
$\mathbb{R}^2$. Journal of Geometric Analysis (2002, volume
12, number 2, 265-288). (pdf)
Preprints/In preparation
(Preprints available on request).
- Diagonal estimates for the Bergman kernel on certain domains in
$\mathbb{C}^n$. (Joint work with Alexander Nagel).
- Measures on monomial polyhedra. (Joint work with Alexander Nagel)
Malabika Pramanik
Last modified: Feb 28 2011