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Radial variation of functions in Besov spaces
Walsh, David (NUI Maynooth (Irlanda). Department of Mathematics)

Data: 2006
Resum: This paper considers the radial variation function F(r, t) of an analytic function f(z) on the disc D. We examine F(r, t) when f belongs to a Besov space As pq and look for ways in which F imitates the behaviour of f. Regarded as a function of position (r, t) in D, we show that F obeys a certain integral growth condition which is the real variable analogue of that satisfied by f. We consider also the radial limit F(t) of F as a function on the circle. Again, F ∈ Bs pq whenever f ∈ As pq, where Bs pq is the corresponding real Besov space. Some properties of F are pointed out along the way, in particular that F(r, t) is real analytic in D except on a small set. The exceptional set E on the circle at which limr→1 f(reit) fails to exist, is also considered; it is shown to have capacity zero in the appropriate sense. Equivalent descriptions of E are also given for certain restricted values of p, q, s.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 50 n. 2 (2006) p. 371-399, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/49972
DOI: 10.5565/PUBLMAT_50206_06

29 p, 260.4 KB

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