homepage of Nicola Arcozzi

RESEARCH INTERESTS: harmonic analysis, complex analysis, geometry of the Heisenberg group
Preprints (.pdf)





Invariance of capacity under quasisymmetric maps of the circle: an easy proof


To appear on a proceeding volume

Potential Theory on Trees, Graphs and Ahlfors Regular Metric Spaces

R.Rochberg,, E. Sawyer, and B. Wick

To appear on Potential Analysis in a revised form

CC-distance and metric normal of smooth hypersurfaces in sub-Riemannian Carnot groups

F.Ferrari,, F. Montefalcone,


Onto interpolating sequences for the Dirichlet space

R.Rochberg,, E. Sawyer,

preliminary version


  Published papers




Capacity of shrinking condensers in the plane

the published paper

Beltrami's models of non-Euclidean geometry

Mathematicians in Bologna 1861–1960, Birkhauser (2012), p.1-29

Distance Functions for Reproducing Kernel Hilbert Spaces

R.Rochberg,, E. Sawyer, and B. Wick

FUNCTION SPACES: Proc. 6th Conf. on Function Spaces, Cont. Math. series of the AMS, vol. 547, 2011

The Dirichlet space: a survey

R.Rochberg,, E. Sawyer, and B. Wick

The published paper. New York Journal of Mathematics, Volume 17a, 2011: Recent Advances in Function Related Operator Theory (Rincon, Puerto Rico, 2010).

Function spaces related to the Dirichlet space

R.Rochberg,, E. Sawyer, and B. Wick

Journal of the London Mathematical Society 2010; doi: 10.1112/jlms/jdq053

Bilinear forms on the Dirichlet space

R.Rochberg,, E. Sawyer, B. Wick

Analysis and PDE, Vol. 3, n. 1, 21-47. Here is the published paper

Two variations on the Drury-Arveson space

R.Rochberg,, E. Sawyer,

CRM Proceedings and Lectures Notes, Vol 51, 2010

Interpolating sequences on analytic Besov type spaces

Daniel Blasi, Jordi Pau

Indiana J. Math. 58, issue 3, 2009

Capacity, Carleson measures, boundary convergence, and exceptional sets

R.Rochberg, E. Sawyer

"Perspective in Harmonic Analysis and Applications" in honor of V.G. Maz'ya 70-th birthday, AMS Proceedings of Symposia in Pure and Applied Mathematics (2008)

Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls

R.Rochberg, E. Sawyer

Adv. Math. (2008) (here is the published paper)

Some problems on Carleson measures for Besov-Sobolev spaces

R.Rochberg, and E. Sawyer

Topics in Complex Analysis and Operator Theory, Proceedings of the Winter School held in Antequera, Malaga, Spain (February 5-9 2006), p. 141-148.

The Hessian of the distance from a surface in the Heisenberg group

F. Ferrari

Ann. Acad. Sci. Fenn. Math., Volumen 33, 2008, 35-63 (here is the published paper)

 Stability of isometric maps in the Heisenberg group

D. Morbidelli

Comm. Math. Helvetici, Volume 83, Issue 1, 2008, pp. 101-141 (here is the published paper)  

From Gruschin to Heisenberg via an isoperimetric problem, fig.1, fig.2

A. Baldi

JMAA, Volume 340, Issue 1, 1 April 2008, Pages 165-174
(here is the published paper)

The characterization of the Carleson measures for analytic Besov spaces: a simple proof

R.Rochberg, E. Sawyer

A. CARBERRY, P. L. DUREN, D. KHAVINSON, A. G. SISKAKIS eds. Complex and Harmonic Analysis. An international conference. Thessaloniki, Greece. 25-27 maggio 2006. Destech Publications Inc. p. 1 - 12.

The Diameter Space:, a restriction of the Drury-Arveson-Hardy space

R.Rochberg, E. Sawyer

Function Spaces, Edited by Krzysztof Jarosz (Proceeding of a conference  held at Southern Illinois University at Edwardsville, IL), Contemporary Mathematics vol. 435, (2007)  p.21-42.

Metric normal and distance function in the Heisenberg group (363Kb)

F. Ferrari

Math. Z., Volume 256, Number 3 / July, 2007 (2007)
(here is the published paper)

A global Inverse Map Theorem and biLipschitz maps in the Heisenberg group

D. Morbidelli

Annali dell'Universita di Ferrara, Volume 52, Number 2 / November, 2006,173-482

Hardy's inequalities for monotone functions on partially ordered measure spaces 

S. Barza, J. L. Garcia-Domingo, J. Soria

Proc. Royal Soc. Edinb. A.  136 (2006) n.5
pp. 909-919(11)

 Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls

R.Rochberg, E. Sawyer

Mem. Amer. Math. Soc. 182 (2006), no. 859, vi+163 pp.

A potential theoretic approach to twisting. 

 F. Di Biase,
M. Picardello

Current trends in potential theory, 3--15,
Theta Ser. Adv. Math., 4, Theta, Bucharest, (2005).

Twist points for planar domains

 F. Di Biase,
M. Picardello

Trans. Amer. Math. Soc. (2006)

Carleson measures for the analytic Besov spaces: the upper triangle case

JIPAM. J. Inequal. Pure Appl. Math. 6 (2005), no. 1,
Article 60, 33 pp. (electronic)

Topics in dyadic Dirichlet spaces


New York J. of Math. 10 (2004)

Large classes of minimally supported frequency wavelets of $L\sp 2(\Bbb R)$ and $H\sp 2(\Bbb R)$.

B. Behera; S. Madan,

J. Geom. Anal. 13 (2003), no. 4, 557--579.

Dominating sets for analytic and harmonic functions
 and completeness of weighted Bergman spaces

A. Bjorn

Math. Proc. Royal Irish Acad.
102A (2002), n.2

Carleson measures for analytic Besov spaces.

R. Rochberg; E. Sawyer

Rev. Mat. Iberoamericana
18 (2002), no. 2, 443--510 

$L\sp p$ estimates for systems of conjugate harmonic functions.

 Complex analysis and differential equations
(Uppsala, 1997),
61--68, Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., 64, Uppsala Univ., Uppsala, 1999

A characterization of the Hilbert transform

L. Fontana

Proc. Amer. Math. Soc. 126 (1998), n.6

Riesz transforms on compact Lie groups, spheres and Gauss space.

Ark. Mat. 36 (1998), no. 2, 201--231

Riesz transforms on spheres

Li, Xinwei

Math. Res. Lett. 4 (1997), no. 3, 401--412

Approach regions for trees and the unit disc.

F. Di Biase; R. Urbanke

J. Reine Angew. Math. 472 (1996), 157--175


Seminars and unpublished

Distance from a curve in the Heisenberg group (preliminary version)

seminario Pini 2012 (here is a beamer of a talk at the annual meeting of the Italian Harmonicists, with pictures and misprints)

Capacita' d'insiemi: diadica e non

Comunicazione al XIX Congresso UMI, Bologna 12-17/09/2011

Carleson measures and Potential Theory: lect.1, lect.2, lect.3, lect.4, lect.5.

Lectures for the The Dirichlet Space: Connections between Operator Theory, Function Theory, and Complex Analysis, Summer Graduate Workshop at MSRI (June 20, 2011 to July 1, 2011). Videos and notes of the lectures in the school are here.


Topix in Math, Bologna 17/06/2011 (seminario espositivo, in italiano)

Spaces related to the Dirichlet Space

Convegno Nazionale di Analisi Armonica 2011; Roma, 31/05/11 (beamer)

Capacita' d'insiemi per alberi, grafi e spazi metrici Ahlfors-regolari

seminario Pini 2010 (italian)

Function spaces related to the Dirichlet space.

Oberwolfach report, 2010

Estimates for the infinite dimensional Drury-Arveson space.

Oberwolfach problem session, 2010

Bordi e interni.

Topix in Math, Bologna 2010, in italian (ci sono un paio di misprint almeno)

Lo spazio di Drury-Arveson: tra analisi complessa, teoria degli operatori e geometria subriemanniana.

seminario Pini 2008 (italian)

Normale metrica e regolarita` della funzione distanza sul gruppo di Heisenberg

seminario Pini 2005 (italian)

Alcune disuguaglianze che vanno nel senso sbagliato

seminario Pini 2004 (italian)

Disuguaglianze di Sobolev per funzioni olomorfe, con applicazioni

seminario Pini 2001 (italian)

Spectral theory on spheres and Gauss space

unpublished notes, 1996.


cnaa1.pdf, cnaa2.pdf, cnaa3.pdf, cnaa3a.pdf, cnaa3b.pdf, cnaa4.pdf, cnaa5.pdf, cnaa6.pdf, cnaa7.pdf, cnaa8.pdf.