Debraj Chakrabarti

activity

20062026

most cited

L^{p}

-regularity of the Bergman projection on quotient domains

23 citations · 78 across the 29 of their papers we have counts for

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33 papers · 1 filter

math.CV2026

The $L^{p}$ - regularity problem for the Bergman projection of two-dimensional Rudin ball quotients

Debraj Chakrabarti, Alessandro Monguzzi

We solve the $L^{p}$ -regularity problem of the Bergman projection of two-dimensional Rudin ball quotients.

math.CV2024

The $\partial ˉ$ -problem on $Z (q)$ -domains

Debraj Chakrabarti, Phillip S. Harrington, Andrew Raich

Given a complex manifold containing a relatively compact $Z (q)$ domain, we give sufficient geometric conditions on the domain so that its $L^{2}$ -cohomology in degree $(p, q)$ (known…

math.CV2023

Bergman kernels of Monomial Polyhedra

Debraj Chakrabarti, Isaac Cinzori, Ishani Gaidhane +2

The Bergman kernels of monomial polyhedra are explicitly computed. Monomial polyhedra are a class of bounded pseudoconvex Reinhardt domains defined as sublevel sets of Laurent mono…

math.CV2023★ 7 cited

Projections onto $L^{p}$ -Bergman spaces of Reinhardt Domains

Debraj Chakrabarti, Luke D. Edholm

For $1 < p < \infty$ , we emulate the Bergman projection on Reinhardt domains by using a Banach-space basis of $L^{p}$ -Bergman space. The construction gives an integral kernel generalizin…

math.CV2021★ 1 cited

Power series as Fourier series

Debraj Chakrabarti, Anirban Dawn

An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fejér's theorem is proved for these series. The theory is applied to dis…

math.CV2020

Exact sequences and estimates for the $\partial$ -problem

Debraj Chakrabarti, Phil Harrington

We study Sobolev estimates for solutions of the inhomogenous Cauchy-Riemann equations on annuli in $\cx^n$, by constructing exact sequences relating the Dolbeault cohomology of the…

math.CV2020★ 23 cited

$L^{p}$ -regularity of the Bergman projection on quotient domains

Chase Bender, Debraj Chakrabarti, Luke D. Edholm +1

We obtain sharp ranges of $L^{p}$ -boundedness for domains in a wide class of Reinhardt domains representable as sub-level sets of monomials, by expressing them as quotients of simple…

math.CV2019★ 17 cited

Bergman Kernels of Elementary Reinhardt Domains

Debraj Chakrabarti, Austin Konkel, Meera Mainkar +1

We study the Bergman kernel of certain domains in $C^{n}$ , called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt do…

math.CV2018★ 2 cited

A Modified Morrey-Kohn-Hörmander Identity and Applications

Debraj Chakrabarti, Phillip S. Harrington

We prove a modified form of the classical Morrey-Kohn-Hörmander identity, adapted to pseudoconcave boundaries. Applying this result to an annulus between two bounded pseudoconvex d…

math.CV2018

On an observation of Sibony

Debraj Chakrabarti

It is shown that if the boundary of a Reinhardt domain in $C^{n}$ contains the origin, each holomorphic function on the domain which is infinitely many times differentiable…

math.CV2018

Fourier Representations in Bergman Spaces

Debraj Chakrabarti, Pranav Upadrashta

We consider a class of domains, generalizing the upper half-plane, and admitting rotational, translational and scaling symmetries, analogous to the half-plane. We prove Paley-Wiene…

math.CV2018★ 18 cited

Duality and approximation of Bergman spaces

D. Chakrabarti, L. D. Edholm, J. D. McNeal

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $C^{n}$ , via examples. When the domain admits an operator satisfying certain…

math.CV2017★ 2 cited

The restriction operator on Bergman spaces

Debraj Chakrabarti, Sonmez Sahutoglu

We study the restriction operator from the Bergman space of a domain in $C^{n}$ to the Bergman space of a non-empty open subset of the domain. We relate the restriction oper…

math.CV2017

Proper holomorphic self-maps of symmetric powers of balls

Debraj Chakrabarti, Christopher Grow

We show that each proper holomorphic self map of a symmetric power of the unit ball is an automorphism naturally induced by an automorphism of the unit ball, provided the ball is o…

math.CV2016

On the $L^{2}$ -Dolbeault cohomology of annuli

Debraj Chakrabarti, Christine Laurent-Thiébaut, Mei-Chi Shaw

For certain annuli in $C^{n}$ , $n \geq 2$ , with non-smooth holes, we show that the $\partial ˉ$ -operator from $L^{2}$ functions to $L^{2}$ $(0, 1)$ -forms has closed range. The…

math.CV2015

Distributional Boundary Values: Some New Perspectives

Debraj Chakrabarti, Rasul Shafikov

We discuss without proof some recent advances in the theory of distributional boundary values, and give an example to show that the condition that a piecewise smooth domain has gen…

math.CV2015

Distributional boundary values of holomorphic functions on product domains

Debraj Chakrabarti, Rasul Shafikov

We show that holomorphic functions of polynomial growth on domains with corners have distributional boundary values in an appropriate sense, provided the corners are generic CR man…

math.CV2015

Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology

Debraj Chakrabarti

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological…

math.CV2014★ 1 cited

$L^{p}$ Mapping Properties of the Bergman Projection on the Hartogs Triangle

Debraj Chakrabarti, Yunus E. Zeytuncu

We prove optimal estimates for the mapping properties of the Bergman projection on the Hartogs triangle in weighted $L^{p}$ spaces when $p > \frac{4}{3}$ , where the weight is a power o…

math.CV2014★ 1 cited

Hölder estimates for Cauchy-Type Integrals and proper holomorphic mappings of symmetric products

Evan Castle, Debraj Chakrabarti, David Gunderman +1

We prove estimates in Hölder spaces for some Cauchy-type integral operators representing holomorphic functions in Cartesian and symmetric products of planar domains. As a consequen…

math.CV2013

Function theory and holomorphic maps on symmetric products of planar domains

Debraj Chakrabarti, Sushil Gorai

We show that the $\partial ˉ$ -problem is globally regular on a domain in $C^{n}$ , which is the $n$ -fold symmetric product of a smoothly bounded planar domain. Remmert-St…

math.CV2013

The $L^{2}$ -cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff

Debraj Chakrabarti, Mei-Chi Shaw

We give an example of a pseudoconvex domain in a complex manifold whose $L^{2}$ -Dolbeault cohomology is non-Hausdorff, yet the domain is Stein. The domain is a smoothly bounded Levi-…

math.CV2012

Condition R and holomorphic mappings of domains with generic corners

Debraj Chakrabarti, Kaushal Verma

A piecewise smooth domain is said to have generic corners if the corners are generic CR manifolds. It is shown that a biholomorphic mapping from a piecewise smooth pseudoconvex dom…

math.CV2012

Condition R and proper holomorphic maps between equidimensional product domains

Debraj Chakrabarti, Kaushal Verma

We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of…

The Lp- regularity problem for the Bergman projection of two-dimensional Rudin ball quotients

The ∂ˉ-problem on Z(q)-domains

Bergman kernels of Monomial Polyhedra

Projections onto Lp-Bergman spaces of Reinhardt Domains

Power series as Fourier series

Exact sequences and estimates for the ∂-problem

Lp-regularity of the Bergman projection on quotient domains

Bergman Kernels of Elementary Reinhardt Domains

A Modified Morrey-Kohn-Hörmander Identity and Applications

On an observation of Sibony

Fourier Representations in Bergman Spaces

Duality and approximation of Bergman spaces

The restriction operator on Bergman spaces

Proper holomorphic self-maps of symmetric powers of balls

On the L2-Dolbeault cohomology of annuli

Distributional Boundary Values: Some New Perspectives

Distributional boundary values of holomorphic functions on product domains

Some non-pseudoconvex domains with explicitly computable non-Hausdorff Dolbeault cohomology

Lp Mapping Properties of the Bergman Projection on the Hartogs Triangle

Hölder estimates for Cauchy-Type Integrals and proper holomorphic mappings of symmetric products

Function theory and holomorphic maps on symmetric products of planar domains

The L2-cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff

Condition R and holomorphic mappings of domains with generic corners

Condition R and proper holomorphic maps between equidimensional product domains

The $L^{p}$ - regularity problem for the Bergman projection of two-dimensional Rudin ball quotients

The $\partial ˉ$ -problem on $Z (q)$ -domains

Projections onto $L^{p}$ -Bergman spaces of Reinhardt Domains

Exact sequences and estimates for the $\partial$ -problem

$L^{p}$ -regularity of the Bergman projection on quotient domains

On the $L^{2}$ -Dolbeault cohomology of annuli

$L^{p}$ Mapping Properties of the Bergman Projection on the Hartogs Triangle

The $L^{2}$ -cohomology of a bounded smooth Stein Domain is not necessarily Hausdorff