Weak-type (1,1) bounds for oscillatory singular integrals with rational phases

• Autorzy: Magali Folch-Gabayet , James Wright
• Języki publikacji: EN

Abstrakty

EN

We consider singular integral operators on ℝ given by convolution with a principal value distribution defined by integrating against oscillating kernels of the form $e^{iR(x)}/x$ where R(x) = P(x)/Q(x) is a general rational function with real coefficients. We establish weak-type (1,1) bounds for such operators which are uniform in the coefficients, depending only on the degrees of P and Q. It is not always the case that these operators map the Hardy space H¹(ℝ) to L¹(ℝ) and we will characterise those rational phases R(x) = P(x)/Q(x) which do map H¹ to L¹ (and even H¹ to H¹).

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 1
• Strony: 57-76

Daty

wydano

2012

Twórcy

autor

Magali Folch-Gabayet

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., 04510, México

autor

James Wright

• Maxwell Institute of Mathematical Sciences and the School of Mathematics, University of Edinburgh, JCMB, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland

Identyfikatory

DOI

10.4064/sm210-1-4