Estimates for oscillatory singular integrals on Hardy spaces

• Autorzy: Hussain Al-Qassem , Leslie Cheng , Yibiao Pan
• Języki publikacji: EN

Abstrakty

EN

For any n ∈ ℕ, we obtain a bound for oscillatory singular integral operators with polynomial phases on the Hardy space H¹(ℝⁿ). Our estimate, expressed in terms of the coefficients of the phase polynomial, establishes the H¹ 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 A₁.

Kategorie tematyczne

• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 224
• Numer: 3
• Strony: 277-289

Daty

wydano

2014

Twórcy

autor

Hussain Al-Qassem

• Department of Mathematics and Physics, Qatar University, Doha, Qatar

autor

Leslie Cheng

• Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, U.S.A.

autor

Yibiao Pan

• Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.

Identyfikatory

DOI

10.4064/sm224-3-5