Rough oscillatory singular integrals on ℝⁿ

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

Abstrakty

EN

We establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. The kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log deg(P), which is optimal and was first obtained by Papadimitrakis and Parissis (2010) for kernels without any radial roughness. Among key ingredients of our methods are an L¹ → L² estimate and extrapolation.

Kategorie tematyczne

• 26D05: Inequalities for trigonometric functions and polynomials
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 3
• Strony: 249-267

Daty

wydano

2014

Twórcy

autor

Hussain Mohammad 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/sm221-3-4