Estimates for oscillatory singular integrals on Hardy spaces

Tom 224 / 2014

Hussain Al-Qassem, Leslie Cheng, Yibiao Pan Studia Mathematica 224 (2014), 277-289 MSC: Primary 42B20; Secondary 42B30. DOI: 10.4064/sm224-3-5


For any $n \in \mathbb {N}$, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space $H^1(\mathbb {R}^n)$. Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the $H^1$ boundedness of such operators in all dimensions when the degree of the phase polynomial is greater than one. It also subsumes a uniform boundedness result of Hu and Pan (1992) for phase polynomials which do not contain any linear terms. Furthermore, the bound is shown to be valid on weighted Hardy spaces as well if the weights belong to the Muckenhoupt class $A_1$.


  • Hussain Al-QassemDepartment of Mathematics and Physics
    Qatar University
    Doha, Qatar
  • Leslie ChengDepartment of Mathematics
    Bryn Mawr College
    Bryn Mawr, PA 19010, U.S.A.
  • Yibiao PanDepartment of Mathematics
    University of Pittsburgh
    Pittsburgh, PA 15260, U.S.A.

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