Carleson measures for analytic Besov spaces: the upper triangle case. (English) Zbl 1127.30313

For a positive weight \(\rho\) on the unit disk \(\mathbb D\) and \(1<p<\infty\), let \(B_p(\rho)\) be the Besov-type space of all holomorphic functions \(f\) in \(\mathbb D\) for which \[ \| f\| := \left(\int_{\mathbb D}\left| (1-| z| ^2)f '(z)\right| ^p \rho(z)\frac{m(dz)}{(1-| z| ^2)^2}+| f(0)| ^p\right)^{1/p} <\infty \] For certain admissible weights the author characterizes those measures \(\mu\) on \(\mathbb D\) for which there exists a constant \(C(\mu)\) such that \(\| f\| _{L^q(\mu)}\leq C(\mu)\| f\| \) for all \(f\in B_p(\rho)\) whenever \(1<q<p<\infty\) (the so called upper triangle case). The case \(1<p\leq q<\infty\) appears in [N. Arcozzi, R. Rochberg and E. Sawyer, Rev. Iberoam. 18, 433–510 (2002; Zbl 1059.30051)].


30H05 Spaces of bounded analytic functions of one complex variable
46E15 Banach spaces of continuous, differentiable or analytic functions


Zbl 1059.30051
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