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

[11] Moduli spaces of abelian differentials: The principal boundary, counting problems, and the Siegel-Veech constants
Eskin, A
Masur, H
Zorich, A
PUBLICATIONS MATHEMATIQUES DE L'IHES, NO 97, 2003, 97 (1): : 61 - 179
[12] Convergence of Siegel–Veech constants
Benjamin Dozier
Geometriae Dedicata, 2019, 198 : 131 - 142
[13] Some Lp(L∞)- and L2(L2)-estimates for oscillatory Fourier transforms
Walther, BG
ANALYSIS OF DIVERGENCE: CONTROL AND MANAGEMENT OF DIVERGENT PROCESSES, 1999, : 213 - 231
[14] Anisotropic shearlet transforms for L2(Rk)
Czaja, Wojciech
King, Emily J.
MATHEMATISCHE NACHRICHTEN, 2014, 287 (8-9) : 903 - 916
[15] L2 BOUNDEDNESS OF HILBERT TRANSFORMS ALONG SURFACES
NAGEL, A
WAINGER, S
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (03): : A413 - A413
[16] A CHARACTERIZATION OF FOURIER-TRANSFORMS IN L2(R)
NASR, AH
APPLICABLE ANALYSIS, 1982, 13 (02) : 87 - 91
[17] A NOTE ON DERIVATIVES OF FUNCTION AND THEIR FOURIER TRANSFORMS IN L2
周晓钟
刘兴权
Applied Mathematics and Mechanics(English Edition), 1990, (01) : 53 - 61
[18] Large Genus Asymptotics for Siegel–Veech Constants
Amol Aggarwal
Geometric and Functional Analysis, 2019, 29 : 1295 - 1324
[19] Measures with Fourier Transforms in L2 of a Half-space
Shayya, Bassam
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2011, 54 (01): : 172 - 179
[20] Vanishing Fourier Transforms and Generalized Differences in L2 (R)
Nillsen, Rodney
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2019, 62 (02): : 393 - 404

← 1 2 3 4 5 →