Carleson Measures and Interpolating Sequences for Besov Spaces on Complex Balls
- ISBN-10
- 0821839179
- ISBN-13
- 9780821839171
- Category
- Besov spaces
- Pages
- 163
- Language
- English
- Published
- 2006
- Publisher
- American Mathematical Soc.
- Authors
- Nicola Arcozzi, Richard Rochberg, Eric T. Sawyer
Description
We characterize Carleson measures for the analytic Besov spaces $B_{p}$ on the unit ball $\mathbb{B}_{n}$ in $\mathbb{C}^{n}$ in terms of a discrete tree condition on the associated Bergman tree $\mathcal{T}_{n}$. We also characterize the pointwise multipliers on $B_{p}$ in terms of Carleson measures. We then apply these results to characterize the interpolating sequences in $\mathbb{B}_{n}$ for $B_{p}$ and their multiplier spaces $M_{B_{p}}$, generalizing a theorem of Boe in one dimension.The interpolating sequences for $B_{p}$ and for $M_{B_{p}}$ are precisely those sequences satisfying a separation condition and a Carleson embedding condition. These results hold for $1\less p \less \infty$ with the exceptions that for $2+\frac{1}{n-1}\leq p
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