Per citar aquest document:
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 ; publishedVersion
Publicat a: Publicacions Matemàtiques, V. 50 n. 2 (2006) p. 371-399, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_50206_06

29 p, 260.4 KB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca

 Registre creat el 2006-11-15, darrera modificació el 2016-06-12

   Favorit i Compartir