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

[21] Sharp L2 log L inequalities for the Haar system and martingale transforms
Osekowski, Adam
STATISTICS & PROBABILITY LETTERS, 2014, 94 : 91 - 97
[22] Trimmed sums of twists and the area Siegel–Veech constant
Vaibhav Gadre
manuscripta mathematica, 2021, 166 : 91 - 99
[23] Integral Transforms of Functionals in L2(Ca,b[0,T])
Seung Jun Chang
Hyun Soo Chung
David Skoug
Journal of Fourier Analysis and Applications, 2009, 15 : 441 - 462
[24] L2 boundedness of Hilbert transforms along variable flat curves
Li, Junfeng
Yu, Haixia
MATHEMATISCHE ZEITSCHRIFT, 2021, 298 (3-4) : 1573 - 1591
[25] L2 ASYMPTOTES FOR FOURIER TRANSFORMS OF SURFACE-CARRIED MEASURES
NELSON, S
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 28 (01) : 134 - &
[26] THEOREM ON SUPPORT OF FUNCTIONS IN L2(IR) AND OF THEIR FOURIER-TRANSFORMS
BERTHIER, AM
JAUCH, JM
LETTERS IN MATHEMATICAL PHYSICS, 1976, 1 (02) : 93 - 97
[27] L2 EXPANSIONS IN TERMS OF GENERALIZED HEAT POLYNOMIALS AND OF THEIR APPELL TRANSFORMS
HAIMO, DT
PACIFIC JOURNAL OF MATHEMATICS, 1965, 15 (03) : 865 - &
[28] Continuous wavelet transforms on the space L2 (R, H; dx)
He, JX
Yu, B
APPLIED MATHEMATICS LETTERS, 2004, 17 (01) : 111 - 121
[29] Two-dimensional fractional shearlet transforms in L2 (R2)
Lone, Waseem Z.
Shah, Firdous A.
Zayed, Ahmed, I
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2022, 25 (06) : 2554 - 2575
[30] Siegel–Veech Constants for Strata of Moduli Spaces of Quadratic Differentials
Elise Goujard
Geometric and Functional Analysis, 2015, 25 : 1440 - 1492

← 1 2 3 4 5 →