SIEGEL-VEECH TRANSFORMS ARE IN L2

被引：9

作者：

Athreya, Jayadev S. ^{[1
]}

Cheung, Yitwah ^{[2
]}

Masur, Howard ^{[3
]}

Ruhr, Rene ^{[4
]}

机构：

[1] Univ Washington, Dept Math, Padelford Hall, Seattle, WA 98195 USA

[2] San Francisco State Univ, Dept Math, Thornton Hall 937,1600 Holloway Ave, San Francisco, CA 94132 USA

[3] Univ Chicago, Dept Math, 5734 South Univ Ave, Chicago, IL 60615 USA

[4] Technion, Fac Math, IL-32000 Haifa, Israel

来源：

JOURNAL OF MODERN DYNAMICS | 2019年 / 14卷

关键词：

Siegel-Veech transform; Abelian differentials; HAUSDORFF DIMENSION; FLOWS; SPACE;

D O I：

10.3934/jmd.2019001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let H denote a connected component of a stratum of translation surfaces. We show that the Siegel-Veech transform of a bounded compactly supported function on R-2 is in L-2(H, mu), where mu is the Lebesgue measure on H, and give applications to bounding error terms for counting problems for saddle connections. We also propose a new invariant associated to SL(2, R)-invariant measures on strata satisfying certain integrability conditions.

引用

页码：1 / 19

页数：19

共 50 条

[41] Volumes of Strata of Abelian Differentials and Siegel–Veech Constants in Large Genera
Eskin A.
Zorich A.
Arnold Mathematical Journal, 2015, 1 (4) : 481 - 488
[42] L2,z ⊗ L2,Z does not embed in L2,z
Brownlowe, Nathan
Sorensen, Adam P. W.
JOURNAL OF ALGEBRA, 2016, 456 : 1 - 22
[43] Convolution products, integral transforms and inverse integral transforms of functionals in L2(C0[0, T])
Chang, Seung Jun
Chung, Hyun Soo
Skoug, David
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2010, 21 (02) : 143 - 151
[44] NAMIAS FRACTIONAL FOURIER-TRANSFORMS ON L2 AND APPLICATIONS TO DIFFERENTIAL-EQUATIONS
KERR, FH
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 136 (02) : 404 - 418
[45] Sharp L2 bound of maximal Hilbert transforms over arbitrary sets of directions
Kim, Joonil
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 335 (01) : 56 - 63
[46] Asymptotic Uniqueness of Best Rational Approximants to Complex Cauchy Transforms in L2 of the Circle
Baratchart, Laurent
Yattselev, Maxim
RECENT TRENDS IN ORTHOGONAL POLYNOMIALS AND APPROXIMATION THEORY, 2010, 507 : 87 - 111
[47] FOURIER-WIENER TRANSFORMS OF FUNCTIONALS BELONGING TO L2 OVER THE SPACE C
CAMERON, RH
MARTIN, WT
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1947, 53 (01) : 51 - 51
[48] Stability of sublevel set estimates and sharp L2 regularity of radon transforms in the plane
Greenblatt, M
MATHEMATICAL RESEARCH LETTERS, 2005, 12 (01) : 1 - 17
[49] Discrete analogues in harmonic analysis -: I:: l2 estimates for singular radon transforms
Stein, EM
Wainger, S
AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (06) : 1291 - 1336
[50] Quasi L2/L2 Hankel Norms and L2/L2 Hankel Norm/Operator of Sampled-Data Systems
Hagiwara, Tomomichi
Hara, Hiroki
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2023, 68 (07) : 4428 - 4434

← 1 2 3 4 5 →