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Decompositions ofLpand Hardy Spaces of Polyharmonic Functions

✍ Scribed by Miroslav Pavlović

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
186 KB
Volume
216
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let H 0p, q F ϱ, yϱ -␣ -ϱ denote the space of those polyhark monic functions f of order k on the unit n-ball for which the function r ¬ Ž . ␣ y 1 rq Ž . q Ž . 1yr

M f ,r belongs to L 0, 1 . Our main result is that, when k G 2 and p Ž . ␣)y 1, the operator f ¬ Pf, ⌬ f , where Pf is the Poisson integral of f, acts as an isomorphism of H p, q, ␣ onto the direct sum of H p, q, ␣ and H p, q, ␣q2 . Another k 1 ky1 decomposition theorem, closely related to the Almansi representation theorem, is also given. ᮊ 1997 Academic Press H p ½ 5 S where d␦ is the normalized surface measure on S s Ѩ B.

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