ISSN:
1432-1785
Keywords:
Mathematics Subject Classification (1991):30D50, 31A20, 30H05, 46E15
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract: For , let and be the spaces of multipliers of , the Sobolev space on the unit circle, and , the Dirichlet type space on the open unit disk, respectively. In fact, and are obtained from and by analytic extension. In this paper, we show that if is an -Carleson measure on the open unit disk, then there exists a function f defined on the closed unit disk such that the equation holds on the open unit disk, and such that the boundary value function f belongs to . For applications, we first establish the corona theorem for , which, in the case , gives the answer to a question of L. Brown and A. L. Shields. Secondly, we obtain a geometric characterization of the interpolating sequences for with that extends a theorem of D. E. Marshall and C. Sundberg.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002290050098
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