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
- Scattering theory, applications to mathematical physics.
Background
I got my Ph.D. 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 since
January 2005. (For more details, here is a copy of my CV in PDF format).
Publications
- Double Hilbert transform
along real-analytic surfaces in $\mathbb{R}^{d+2}$.
(Joint work with Chan Woo Yang) Submitted. (pdf)
- Averages over curves in
$\mathbb{R}^3$ and associated maximal functions.
(Joint work with Andreas Seeger) To appear in Amer. J. Math. (pdf)
- $L^p$ Sobolev regularity of
a restricted X-ray transform. (Joint work with
Andreas Seeger) To appear in Harmonic
Analysis and its Applications at Osaka, Conference
Proceedings 2004. (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) To appear
in Revista Matematica Iberoamericana. (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).
- Maximal averages over linear and monomial polyherda. (Joint work
with Alexander Nagel).
- 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)
- Oscillatory integral operators with homogeneous polynomial phases
in several variables. (Joint work with Allan Greenleaf and
Wan Tang).
Malabika Pramanik
Last modified: Thu May 4 13:46:49 PDT 2006