Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels

Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels

We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition im...

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Bibliographic Details
Main Authors: Hussain Al-Qassem, Leslie Cheng, Yibiao Pan
Format: Article
Language:English
Published: Hindawi Limited 2019-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2019/8561402
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spelling doaj-e22e96d949fb4456903680afcda84faa2020-11-25T00:28:54ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/85614028561402Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class KernelsHussain Al-Qassem0Leslie Cheng1Yibiao Pan2Department of Mathematics and Physics, Qatar University, Doha, QatarDepartment of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USADepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USAWe prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature.http://dx.doi.org/10.1155/2019/8561402
collection DOAJ
language English
format Article
sources DOAJ
author Hussain Al-Qassem
Leslie Cheng
Yibiao Pan
spellingShingle Hussain Al-Qassem
Leslie Cheng
Yibiao Pan
Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
Journal of Function Spaces
author_facet Hussain Al-Qassem
Leslie Cheng
Yibiao Pan
author_sort Hussain Al-Qassem
title Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
title_short Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
title_full Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
title_fullStr Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
title_full_unstemmed Endpoint Estimates for Oscillatory Singular Integrals with Hölder Class Kernels
title_sort endpoint estimates for oscillatory singular integrals with hölder class kernels
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2019-01-01
description We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature.
url http://dx.doi.org/10.1155/2019/8561402
work_keys_str_mv AT hussainalqassem endpointestimatesforoscillatorysingularintegralswithholderclasskernels
AT lesliecheng endpointestimatesforoscillatorysingularintegralswithholderclasskernels
AT yibiaopan endpointestimatesforoscillatorysingularintegralswithholderclasskernels
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