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Boundary Values of Harmonic Functions in Spaces of Triebel–Lizorkin Type

✍ Scribed by Lin, Chin-Cheng; Lin, Ying-Chieh


Book ID
125338200
Publisher
SP Birkhäuser Verlag Basel
Year
2014
Tongue
English
Weight
368 KB
Volume
79
Category
Article
ISSN
0378-620X

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## Abstract We study the maximal function M__f__(__x__) = sup |__f__(__x__ + __y, t)|__ when Ω is a region in the (__y,t__) Ω upper half space R and __f(x, t__) is the harmonic extension to R~+~__^N+1^__ of a distribution in the Besov space B^α^__~p,q~__(R__^N^__) or in the Triebel‐Lizorkin space F

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In 1938 S.L. Sobolev proved his well-known embedding theorem for domains G ⊂ R n satisfying the cone condition (see [1]). Relation (2) (which determines the maximum possible value of q in theorem ( 1)) is also a necessary condition for the embedding. Sobolev's result has been extended to domains of