Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A class of $P^t(d\mu )$ spaces whose point evaluations vary with

Author(s): John Akeroyd; Elias G. Saleeby
Journal: Proc. Amer. Math. Soc. 127 (1999), 537-542.
MSC (1991): Primary 30E10, 46E15
MathSciNet review: 1473652
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Abstract: Extending an example given by T. Kriete, we develop a class of measures each of which consists of a measure on $\{z:\,|z|{}=1\}$ along with a series of weighted point masses in $\mathbf{D:=}\{z:\,|z|{}<1\}$ . This class provides relatively simple examples of measures $\mu$ which have the property that the collection of analytic bounded point evaluations for $P^{t}(d\mu )$ varies with . The first known measures with this property were recently constructed by J. Thomson.

References:

1.: J. Akeroyd, An extension of Szegö's Theorem II, Indiana Univ. Math. J., Vol. 45, No. 1 (1996), 241-252. MR 97h:30055
2.: T. L. Kriete, Cosubnormal dilation semigroups on Bergman spaces, J. Operator Theory 17 (1987), 191-200. MR 88e:47041
3.: T. L. Kriete and H. C. Rhaly, Translation semigroups on reproducing kernel Hilbert spaces, J. Operator Theory 17 (1987), 33-83. MR 88e:47080
4.: J. Thomson, Approximation in the mean by polynomials, Ann. of Math. (2) 133 (1991), 477-507. MR 93g:47026
5.: J. Thomson, Bounded point evaluations and polynomial approximation, Proc. Amer. Math. Soc., Vol. 123, No. 6 (1995), 1757-1761.MR 95g:30051

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