Lp-Sobolev Estimates for a Class of Integral Operators with Folding Canonical Relations

被引：0

作者：

Pramanik, Malabika ^{[1
]}

Seeger, Andreas ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, Room 121,1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[2] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 07期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Regularity of integral operators; Radon transforms; Fourier integral operators; Folding canonical relations; Sobolev spaces; CURVES; AVERAGES; REGULARITY;

D O I：

10.1007/s12220-020-00388-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a sharp L-p-Sobolev regularity result for a class of generalized Radon transforms for families of curves in a three-dimensional manifold, with folding canonical relations. The proof relies on decoupling inequalities by Wolff and by Bourgain-Demeter for plate decompositions of thin neighborhoods of cones.

引用

页码：6725 / 6765

页数：41

共 50 条

[1] LP-SOBOLEV REGULARITY FOR INTEGRAL OPERATORS OVER CERTAIN HYPERSURFACES
Heo, Yaryong
Hong, Sunggeum
Yang, Chan Woo
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (04) : 965 - 978
[2] On oscillatory integral operators with folding canonical relations
Greenleaf, A
Seeger, A
[J]. STUDIA MATHEMATICA, 1999, 132 (02) : 125 - 139
[3] Canonical potential and Lp-Sobolev space involving linear canonical Fourier transform
Prasad, Akhilesh
Kumar, Amit
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2023, 34 (04) : 295 - 315
[4] Inclusion relations between LP-Sobolev and Wiener amalgam spaces
Cunanan, Jayson
Kobayashi, Masaharu
Sugimoto, Mitsuru
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 268 (01) : 239 - 254
[5] Estimates of images of Lp-functions for some class of integral operators
Rodionov, T.V.
[J]. Vestnik Moskovskogo Universiteta. Ser. 1 Matematika Mekhanika, 2003, (06): : 7 - 11
[6] LP Regularity Estimates for a Class of Integral Operators with Fold Blowdown Singularities
Bentsen, Geoffrey
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2022, 32 (03)
[7] Lp estimates for oscillatory integral operators
Cheng, LC
Pan, YB
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (10) : 2995 - 3002
[8] Weighted Sobolev L2 estimates for a class of Fourier integral operators
Ruzhansky, Michael
Sugimoto, Mitsuru
[J]. MATHEMATISCHE NACHRICHTEN, 2011, 284 (13) : 1715 - 1738
[9] The inclusion relations between α-modulation spaces and LP-Sobolev spaces or local Hardy spaces
Kato, Tomoya
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (04) : 1340 - 1405
[10] Lp ESTIMATES FOR A CLASS OF DEGENERATE OPERATORS
Metafune, Giorgio
Negro, Luigi
Spina, Chiara
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2024, 17 (5-6): : 1766 - 1791

← 1 2 3 4 5 →