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Maximal functions and subordination for operator groups.

Blower, Gordon (2002) Maximal functions and subordination for operator groups. Proceedings of the Edinburgh Mathematical Society, 45 (1). pp. 27-42. ISSN 0013-0915

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Abstract

Let E be a UMD Banach space and L a positive and self-adjoint operator in L^2 of Laplace type such that the imaginary powers L^{-it} form a C_0 group of exponential growth on L^p(E). Suppose that G is holomorphis inside and on the boundary os a suitable sector. Then G(tL) defines a bounded family of linear operators on L^p(E); the maximal operator f->sup | G(tL)f| os bounded on the domain of log L. These hypotheses hold for the maximal solution operators for the heat, wave and Schroedinger operators, and for Cesaro sums.

Item Type: Article
Journal or Publication Title: Proceedings of the Edinburgh Mathematical Society
Additional Information: AMS 2000 classification 47D03; 42B25; 47D09 The final, definitive version of this article has been published in the Journal, Proceedings of the Edinburgh Mathematical Society, 45 (1), pp 27-42 2002, © 2002 Cambridge University Press.
Uncontrolled Keywords: maximal functions ; transference ; UMD Banach spaces
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 1693
Deposited By: Professor Gordon Blower
Deposited On: 18 Feb 2008 10:06
Refereed?: Yes
Published?: Published
Last Modified: 04 Dec 2016 01:13
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/1693

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