Malabika Pramanik's Research
Areas of interest
 Euclidean harmonic analysis
 Cone multipliers and local smoothing
 Multiparameter 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 (20012004),
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 (March 2016) in
PDF format).
Publications

On the maximal directional Hilbert transform. (Joint work with I. Laba and A. Marinelli)
To appear in Analysis Mathematica

On large sets avoiding patterns. (Joint work with R. Fraser)
Analysis and PDE Volume 11, Number 5 (2018), 10831111.

A discrete Carleson theorem along the primes with a restricted supremum.
(Joint work with L. Cladek, K. Henriot, B. Krause, I. Laba)
Math. Z. (2018) 289: 1033. https://doi.org/10.1007/s0020901719878

A Rothtype theorem for dense subsets of R^d. (Joint work with B. Cook and A. Magyar)
Bulletin of the London Mathematical Society, 49 No.4: 676689 (2017)

Necklaces inside thin sets of R^d. (Joint work with A. Greenleaf and A. Iosevich)
Mathematics Research Letters, 24 No. 2: 347362, 2017.

On polynomial congurations in fractal sets
(Joint work with K. Henriot and I. Laba)
Analysis and PDE, 9 No. 5: 11531184, 2016.

KakeyaType sets over Cantor sets of directions in R^d+1. (Joint work with Edward Kroc)
J. Fourier Anal. Appl. (2016) 22: 623. https://doi.org/10.1007/s000410159426x

Finite configurations in sparse sets. (Joint work with V. Chan and I. Laba)
J. d'Analyse Math. (2016) 128: 289. https://doi.org/10.1007/s1185401600103

Chaotic dynamics of the heat semigroup on Riemannian symmetric spaces. (Joint work with R. Sarkar) J.
Funct. Anal., 266 No. 5: 28672909, 2014.
 A multidimensional resolution of singularities with applications to
analysis. (Joint work with Tristan Collins and Allan Greenleaf) Amer. J. Math., 135 No.5: 11791252, 2013. (arXiv preprint)

Diagonal estimates for the Bergman kernel in monomialtype domains. (Joint work with A. Nagel)
Proceedings of the conference in honor of Eli Stein, Princeton, 2011.
 Maximal operators and differentiation theorems for sparse sets. (Joint work with
Izabella Laba) Duke Math. J., 158 No.3: 347411, 2011.
 An FIO calculus for marine seismic imaging, II: Sobolev estimates (Joint work with
Raluca Felea and Allan Greenleaf) Math. Annalen DOI: 10.1007/s0020801106445.
 A Calder?nZygmund estimate with applications
to generalized Radon transforms and Fourier integral operators. (Joint work with
Keith Rogers and Andreas Seeger) Studia Math., 202 (2011), 115.
 Multilinear singular operators with fractional rank. (Joint work with
Ciprian Demeter and Christoph Thiele) Pacific J. of Mathematics 246 (2010) no. 2, 293324
 Maximal averages over linear and monomial polyhedra. (Joint work
with Alexander Nagel) Duke Math. J. Volume 149 Number 2 (2009), 209277.
 Arithmetic progressions in sets of fractional dimension. (Joint work with
Izabella Laba) Geom. Funct. Anal. 19 (2009), 429456.
 Oscillatory integral operators with homogeneous
polynomial phases in several variables. (Joint work with
Allan Greenleaf and Wan Tang) J. Functional
Analysis (2007, volume 244, 444487). (pdf)
 Double Hilbert transform
along realanalytic surfaces in $\mathbb{R}^{d+2}$.
(Joint work with Chan Woo Yang) J. London Math. Soc. (2008) 77(2):363386.
 Averages over curves in
$\mathbb{R}^3$ and associated maximal functions.
(Joint work with Andreas Seeger) Amer. J. Math. (2007, volume 21, number 3, 61103). (pdf)
 $L^p$ Sobolev regularity of a restricted Xray
transform. (Joint work with Andreas Seeger) Harmonic Analysis and its Applications at Osaka, Conference
Proceedings (November 2004, 4764). (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, 10711095). (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, 613645).
(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,
775813). (pdf)
 Convergence of twodimensional weighted integrals. Transactions
of the American Mathematical Society (2002, volume 354,
number 4, 16511665). (pdf)
 Weighted inequalities for realanalytic functions in
$\mathbb{R}^2$. Journal of Geometric Analysis (2002, volume
12, number 2, 265288). (pdf)
Preprints/In preparation

Lacunarity, Kakeyatype sets and directional maximal operators. (Joint work with E. Kroc)
(arXiv preprint)
 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: Sept 4 2016