Annales Academiæ Scientiarum Fennicæ

Mathematica

Volumen 33, 2008, 303-313

# DISTANCES FROM BLOCH FUNCTIONS
TO SOME MÖBIUS INVARIANT SPACES

## Ruhan Zhao

SUNY-Brockport, Department of Mathematics

Brockport, NY 14420, U.S.A.; rzhao 'at' brockport.edu

**Abstract.**
Distance formulas from Bloch functions
to some Möbius
invariant function spaces are given. These results generalize the
distance formula from Bloch functions to *BMOA* by Peter Jones.
As consequences, we have characterized the closures of these Möbius
invariant function spaces in the Bloch space.

**2000 Mathematics Subject Classification:**
Primary 30D45.

**Key words:**
Bloch functions, *F*(p,q,s) spaces,
*Q*_{p} spaces, Carleson measures, distance.

**Reference to this article:** R. Zhao:
Distances from Bloch functions to some Möbius invariant spaces.
Ann. Acad. Sci. Fenn. Math. 33 (2008), 303-313.

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