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L q-THEORY OF A SINGULAR “WINDING” INTEGRAL OPERATOR ARISING FROM FLUID DYNAMICS

By Reinhard Farwig, Toshiaki Hishida and Detlef Müller

Abstract

We analyze in classical L q (R n)-spaces, n = 2 or n = 3, 1 <q<∞, a singular integral operator arising from the linearization of a hydrodynamical problem with a rotating obstacle. The corresponding system of partial differential equations of second order involves an angular derivative which is not subordinate to the Laplacian. The main tools are Littlewood–Paley theory and a decomposition of the singular kernel in Fourier space

Year: 2004
DOI identifier: 10.2140/pjm.2004.215.297
OAI identifier: oai:CiteSeerX.psu:10.1.1.217.8941
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