Optimal domains for the kernel operator associated with Sobolev's inequality

• Autorzy: Guillermo P. Curbera , Werner J. Ricker
• Języki publikacji: EN

Abstrakty

EN

Refinements of the classical Sobolev inequality lead to optimal domain problems in a natural way. This is made precise in recent work of Edmunds, Kerman and Pick; the fundamental technique is to prove that the (generalized) Sobolev inequality is equivalent to the boundedness of an associated kernel operator on [0,1]. We make a detailed study of both the optimal domain, providing various characterizations of it, and of properties of the kernel operator when it is extended to act in its optimal domain. Several results are devoted to identifying the maximal rearrangement invariant space inside the optimal domain. The methods and techniques used involve interpolation theory, Banach function spaces and vector integration.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 47G10: Integral operators
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 28B05: Vector-valued set functions, measures and integrals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 158
• Numer: 2
• Strony: 131-152

Daty

wydano

2003

Twórcy

autor

Guillermo P. Curbera

• Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain

autor

Werner J. Ricker

• Math.-Geogr. Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85072 Eichstätt, Germany

Identyfikatory

DOI

10.4064/sm158-2-3