@article{Shen2026, 
author = {Jiawei Shen and Jie Yang},
title = {L    p   boundedness of oscillatory singular integrals with nonstandard kernels},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {20254-20266},
keywords = {oscillatory integral, rough kernel, non-standard kernel, Lp spaces, BMO space},
url = {https://www.sciopen.com/article/10.3934/math.2026822},
doi = {10.3934/math.2026822},
abstract = {In this paper, we study a kind of oscillatory singular integral operator        T          P      ,      Ω      ,      A       defined by         T          P      ,      Ω      ,      A        f  (  x  )  =  p.v.      ∫                            R                n                  e          i      P      (      x      −      y      )                  Ω      (      x      −      y      )              [                  A          (          x          )          −          A          (          y          )          −          ∇          A          (          y          )          ⋅          (          x          −          y          )                ]                            |            x      −      y                        |                          n          +          1                      f  (  y  )  d  y  ,where    P  (  x  ) is a real polynomial on              R        n    , and    Ω  (  λ  x  )  =  Ω  (  x  )  . Under some conditions, we show that        T          P      ,      Ω      ,      A       is bounded on        L    p    (            R              n        ) with uniform boundedness, which improves and extends Pan's result [11].}
}