The focus on my research is on the following problems.
- Unique continuation properties of solutions
of elliptic equations and systems.
- Evaluation of the norms of convolution
operators and other sharp constants
- Geometric
properties of harmonic functions and of
solutions of Schrodinger equations
- Restriction properties of the Fourier
transform to manifolds of arbitrary codimension
- The restriction conjecture
- Uniform estimates of orthogonal polynomials
and special functions
Here is a list of my publications and preprints. You can retrieve my recent preprints in .dvi and/or .pdf format.
Papers in Professional Journals
[22] D. Bilyk, L. De Carli, A. Petukhov, A. Stokolos and B.~D. Wick , On The Scientific Work of Konstantin Ilyich Oskolkov , to appear in " Recent Advances in Harmonic Analysis and Applications (In Honor of Konstantin Oskolkov), Springer Proceedings in Mathematics (2012)
[21] L. De Carli, J. Edward, S.
Hudson, M. Leckband, Minimal support results for Schrodinger's equation, (2012). Submitted.
[20] L. De Carli, On Fourier multipliers over tube
domains, to appear in " Recent Advances in
Harmonic Analysis and Applications (In Honor of Konstantin Oskolkov), Springer
Proceedings in Mathematics (2012)
[19] L. De Carli, S. Hudson, A Faber-Krahn inequality for solutions of Schrodinger's equation,. Advances in Mathematics 230 (2012), pp. 2416-2427
[21] L. De Carli, J. Edward, S.
Hudson, M. Leckband, Minimal support results for Schrodinger's equation, (2012). Submitted.
[20] L. De Carli, On Fourier multipliers over tube
domains, to appear in " Recent Advances in
Harmonic Analysis and Applications (In Honor of Konstantin Oskolkov), Springer
Proceedings in Mathematics (2012)
[19] L. De Carli, S. Hudson, A Faber-Krahn inequality for solutions
of Schrodinger's equation, (2010). To appear in Advances in Math.
[18] L. De Carli,
[17] L. De Carli,
42 (2010), n. 1, 83—95 .
[16] L. De Carli, M. Ash, Growth of L^p Lebesgue constants for convex polyhedra and other regions, Transaction of the American Math. Soc. 361 (2009), n. 8, 4215--4232.
[15] L. De Carli, Local L^p inequalities for Gegenbauer polynomials, in Topics in classical analysis and applications in honor of Daniel Waterman, 73--87, World Sci. Publ., Hackensack, NJ, (2008).
[14] L. De Carli,
On
the L^p-L^q norm of the Hankel transform and related operators, J. Math. Anal. Appl. 348 (2008), n. 1, 366--382.
[13] L. De Carli,
[12] L. De Carli, Uniform estimates of ultraspherical
polynomials of large order ,
Canadian Math. Bullettin. 48 (2005), no 3, 382—393.
[11] L. De Carli and L. Grafakos, On the restriction conjecture, Michigan Math. J. 52 (2004), no. 1, 163--180.
[10] L. De Carli and T. Okaji, Strong Unique continuation for Schrodinger operator from a sphere, Houston
J. Math. 27 (2001), no. 1, 219--235.
[9] L. De Carli and E. Laeng, On
the (p,p) norm of monotonic Fourier multipliers, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 8, 657--662.
[1] L. De Carli, Unique continuation for higher order elliptic
operators, Thesis,
[2] L. De
Carli, Funzioni olomorfe a crescenza lenta e problemi
non lineari, (holomorphic functions with slow growth and non linear
problems), Thesis, Universita’ di Roma ``La
sapienza", (1993)
[3] L. De
Carli, L^p estimates for the Cauchy kernel on cones, preprint (1998).