Boundedness properties of fractional integral operators associated to non-doubling measures

• Autorzy: José García-Cuerva , A. Eduardo Gatto
• Języki publikacji: EN

Abstrakty

EN

The main purpose of this paper is to investigate the behavior of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non-doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on Euclidean space and their known extensions for doubling measures. We start by analyzing the images of the Lebesgue spaces associated to the measure. The Lipschitz spaces, defined in terms of the metric, also play a basic role. For a Euclidean space equipped with one of these measures, we also consider the so-called regular BMO space introduced by X. Tolsa. We show that it contains the image of a Lebesgue space in the appropriate limit case and also that the image of the regular BMO space is contained in a suitable Lipschitz space.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 26A33: Fractional derivatives and integrals
• 47G10: Integral operators
• 42B20: Singular and oscillatory integrals (Calder\'on-Zygmund, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 162
• Numer: 3
• Strony: 245-261

Daty

wydano

2004

Twórcy

autor

José García-Cuerva

• Departamento de Matemáticas, C-XV, Universidad Autónoma, 28049, Madrid, Spain

autor

A. Eduardo Gatto

• Department of Mathematics, DePaul University, Chicago, IL 60614, U.S.A.

Identyfikatory

DOI

10.4064/sm162-3-5