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October 1996 Integrability of Green potentials in fractal domains
Kaj Nyström
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Ark. Mat. 34(2): 335-381 (October 1996). DOI: 10.1007/BF02559551


We prove Lq-inequalities for the gradient of the Green potential (Gf) in bounded, connected NTA-domains in Rn, n≥2. These domains may have a highly non-rectifiable boundary and in the plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponent q for which our inequalities are valid in terms of the validity of a reverse Hölder inequality for the Green function close to the boundary.


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Kaj Nyström. "Integrability of Green potentials in fractal domains." Ark. Mat. 34 (2) 335 - 381, October 1996.


Received: 19 October 1995; Published: October 1996
First available in Project Euclid: 31 January 2017

zbMATH: 0860.31002
MathSciNet: MR1416671
Digital Object Identifier: 10.1007/BF02559551

Rights: 1996 © Institut Mittag-Leffler


Vol.34 • No. 2 • October 1996
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