Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-02T23:03:05.189Z Has data issue: false hasContentIssue false
  • English
  • Français

VOLTERRA CONVOLUTION OPERATORS WITH VALUES IN REARRANGEMENT INVARIANT SPACES

Published online by Cambridge University Press:  01 August 1999

GUILLERMO P. CURBERA
GUILLERMO P. CURBERA
Affiliation:
Facultad de Matemáticas, Universidad de Sevilla, Aptdo. (PO Box) 1160, Sevilla 41080, Spain
Get access

Abstract

The Volterra convolution operator [Vscr ]f(x) = ∫x0ϕ (x−y)f(y)dy, where ϕ(·) is a non-negative non-decreasing integrable kernel on [0, 1], is considered. Under certain conditions on the kernel ϕ, the maximal Banach function space on [0, 1] on which the Volterra operator is a continuous linear operator with values in a given rearrangement invariant function space on [0, 1] is identified in terms of interpolation spaces. The compactness of the operator on this space is studied.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 258 - 268
Copyright
The London Mathematical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by DGICYT grant #PB96-1321-C02-01.