Loredana Lanzani

activity

20052025

most citedCauchy-type integrals in several complex variables

31 citations · 99 across the 22 of their papers we have counts for

collaborators

25 papers

math.CV2025

The Cauchy--Szegö Projection for domains in $C^{n}$ with minimal smoothness: weighted theory

Xuan Thinh Duong, Loredana Lanzani, Ji Li +1

Let $D \subset C^{n}$ be a bounded, strongly pseudoconvex domain whose boundary $b D$ satisfies the minimal regularity condition of class $C^{2}$ . A 2017 result of Lanzani \& Stei…

math.CV2024

The Unified Transform Method: beyond circular or convex domains

Jesse J. Hulse, Loredana Lanzani, Stefan G. Llewellyn Smith +1

A new transform-based approach is presented that can be used to solve mixed boundary value problems for Laplace's equation in non-convex and other planar domains, specifically the…

math.CV2024

A new way to express boundary values in terms of holomorphic functions on planar Lipschitz domains

Steven R. Bell, Loredana Lanzani, Nathan A. Wagner

We decompose $p$ - integrable functions on the boundary of a simply connected Lipschitz domain $Ω \subset C$ into the sum of the boundary values of two, uniquely determined…

math.CV2024

Boundary value problems for holomorphic functions on Lipschitz planar domains

William Gryc, Loredana Lanzani, Jue Xiong +1

We study the $\partial ˉ$ equation subject to various boundary value conditions on bounded simply connected Lipschitz domains $D \subset C$ : for the Dirichlet problem with…

math.CV2024

New Properties of Holomorphic Sobolev-Hardy Spaces

William Gryc, Loredana Lanzani, Jue Xiong +1

We give new characterizations of the optimal data space for the $L^{p} (b D, σ)$ -Neumann boundary value problem for the $\partial ˉ$ operator associated to a bounded, Lipschitz doma…

math.CV2023

A transform pair for bounded convex planar domains

Jesse Hulse, Loredana Lanzani, Stefan Llewellyn Smith +1

A new transform pair which can be used to solve mixed boundary value problems for Laplace's equation and the complex Helmholtz equation in bounded convex planar domains is presente…

math.CV2022

The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness

Bingyang Hu, Zhenghui Huo, Loredana Lanzani +2

Consider a bounded, strongly pseudoconvex domain $D \subset C^{n}$ with minimal smoothness (namely, the class $C^{2}$ ) and let $b$ be a locally integrable function on $D$ . We ch…

math.CV2020★ 7 cited

Hardy Spaces for a Class of Singular Domains

Anne-Katrin Gallagher, Purvi Gupta, Loredana Lanzani +1

We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filt…

math.CV2020

The commutator of the Cauchy--Szegő Projection for domains in $C^{n}$ with minimal smoothness: weighted regularity

Xuan Thinh Duong, Loredana Lanzani, Ji Li +1

Let $D \subset C^{n}$ be a bounded, strongly pseudoconvex domain whose boundary $b D$ satisfies the minimal regularity condition of class $C^{2}$ , and let $S_{ω}$ denote the Cauchy-…

math.CV2020

Symmetrization of a Cauchy-like kernel on curves

Loredana Lanzani, Malabika Pramanik

Given a curve $Γ \subset C$ with specified regularity, we investigate boundedness and positivity for a certain three-point symmetrization of a Cauchy-like kernel $K_{Γ}$ whose…

math.CV2020

Symmetrization of a family of Cauchy-Like kernels: Global instability

Loredana Lanzani, Malabika Pramanik

The fundamental role of the Cauchy transform in harmonic and complex analysis has led to many different proofs of its $L^{2}$ boundedness. In particular, a famous proof of Melnikov-V…

math.CV2019★ 6 cited

Regularity of a $\partial ˉ$ -solution operator for strongly $C$ -linearly convex domains with minimal smoothness

Xianghong Gong, Loredana Lanzani

We prove regularity of solutions of the $\partial ˉ$ -problem in the Hölder-Zygmund spaces of bounded, strongly $C$ -linearly convex domains of class $C^{1, 1}$ . The proofs…

math.CV2019★ 2 cited

On regularity and irregularity of certain holomorphic singular integral operators

Loredana Lanzani, Elias M. Stein

We survey recent work and announce new results concerning two singular integral operators whose kernels are holomorphic functions of the output variable, specifically the Cauchy-Le…

math.CV2017

The role of an integration identity in the analysis of the Cauchy-Leray transform

Loredana Lanzani, Elias M. Stein

The purpose of this paper is to complement the results in [LS-1] by showing the dense definability of the Cauchy-Leray transform for the domains that give the counterexamples of [L…

math.CV2017

The Cauchy-Leray integral: counter-examples to the $L^{p}$ -theory

Loredana Lanzani, Elias M. Stein

We prove the optimality of the hypotheses guaranteeing the $L^{p}$ -boundedness for the Cauchy-Leray integral in $C^{n}$ , $n \geq 2$ , obtained in [LS-4]. Two domains, both elemen…

math.AP2015

On Div-Curl for Higher Order

Loredana Lanzani, Andrew S. Raich

We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^{1}$ -duality estimates.

math.CV2015★ 1 cited

Harmonic Analysis Techniques in Several Complex Variables

Loredana Lanzani

We give a survey of recent joint work with E. M. Stein (Princeton University) concerning the application of suitable versions of the T(1)-theorem technique to the study of orthogon…

math.CV2015★ 16 cited

The Cauchy-Szeg\H o projection for domains in $\mathbb C^n% with minimal smoothness

Loredana Lanzani, Elias M. Stein

We prove $L^{p} (b D)$ -regularity of the Cauchy-Szeg\H o projection (also known as the Szeg\H o projection) for bounded domains $D \subset C^{n}$ whose boundary satisfies the mini…

math.CV2015

Hardy spaces of holomorphic functions for domains in $C^{n}$ with minimal smoothness

Loredana Lanzani, Elias M. Stein

We prove various representations and density results for Hardy spaces of holomorphic functions for two classes of bounded domains in $C^{n}$ , whose boundaries satisfy minimal…

math.AP2013★ 2 cited

Higher order analogues of exterior derivative

Loredana Lanzani

We give new examples of linear differential operators of order $k = 2 m + 1$ (any given odd integer) that are invariant under the isometries of $R^{n}$ and satisfy so-called $L^{1}$ …

math.CV2013★ 31 cited

Cauchy-type integrals in several complex variables

Loredana Lanzani, Elias M. Stein

We present the theory of Cauchy-Fantappié integral operators, with emphasis on the situation when the domain of integration, $D$ , has minimal boundary regularity. Among these opera…

math.CV2013★ 1 cited

The Cauchy Integral in $C^{n}$ for domains with minimal smoothness

Loredana Lanzani, Elias M. Stein

We prove $L^{p} (b D)$ -regularity of the Cauchy-Leray integral for bounded domains $D \subset C^{n}$ whose boundary satisfies the minimal regularity condition o…

math.CV2012

The Bergman projection in $L^{p}$ for domains with minimal smoothness

Loredana Lanzani, Elias M. Stein

Let $D \subset C^{n}$ be a bounded, strongly Levi-pseudoconvex domain with minimally smooth boundary. We prove $L^{p} (D)$ -regularity for the Bergman projection $B$ , and for the o…

math.CV2007★ 2 cited

The spectrum of the Leray transform for convex Reinhardt domains in $C^{2}$

David E. Barrett, Loredana Lanzani

The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $C^{2}$ . Our class is self-dual; it contains some domains with less…

The Cauchy--Szegö Projection for domains in Cn with minimal smoothness: weighted theory

The Unified Transform Method: beyond circular or convex domains

A new way to express boundary values in terms of holomorphic functions on planar Lipschitz domains

Boundary value problems for holomorphic functions on Lipschitz planar domains

New Properties of Holomorphic Sobolev-Hardy Spaces

A transform pair for bounded convex planar domains

The Commutator of the Bergman Projection on Strongly Pseudoconvex Domains with Minimal Smoothness

Hardy Spaces for a Class of Singular Domains

The commutator of the Cauchy--Szegő Projection for domains in Cn with minimal smoothness: weighted regularity

Symmetrization of a Cauchy-like kernel on curves

Symmetrization of a family of Cauchy-Like kernels: Global instability

Regularity of a ∂ˉ-solution operator for strongly C-linearly convex domains with minimal smoothness

On regularity and irregularity of certain holomorphic singular integral operators

The role of an integration identity in the analysis of the Cauchy-Leray transform

The Cauchy-Leray integral: counter-examples to the Lp-theory

On Div-Curl for Higher Order

Harmonic Analysis Techniques in Several Complex Variables

The Cauchy-Szeg\H o projection for domains in $\mathbb C^n% with minimal smoothness

Hardy spaces of holomorphic functions for domains in Cn with minimal smoothness

Higher order analogues of exterior derivative

Cauchy-type integrals in several complex variables

The Cauchy Integral in Cn for domains with minimal smoothness

The Bergman projection in Lp for domains with minimal smoothness

The spectrum of the Leray transform for convex Reinhardt domains in C2

The Cauchy--Szegö Projection for domains in $C^{n}$ with minimal smoothness: weighted theory

The commutator of the Cauchy--Szegő Projection for domains in $C^{n}$ with minimal smoothness: weighted regularity

Regularity of a $\partial ˉ$ -solution operator for strongly $C$ -linearly convex domains with minimal smoothness

The Cauchy-Leray integral: counter-examples to the $L^{p}$ -theory

Hardy spaces of holomorphic functions for domains in $C^{n}$ with minimal smoothness

The Cauchy Integral in $C^{n}$ for domains with minimal smoothness

The Bergman projection in $L^{p}$ for domains with minimal smoothness

The spectrum of the Leray transform for convex Reinhardt domains in $C^{2}$