arXiv subjects
Publications and source records attributed to Gerardo R. Chacón.
We introduce a variable exponent version of the Hardy space of analytic functions on the unit disk, we show some properties of the space, and give an example of a variable exponent $p(\cdot)$ that satisfies the $\log$-Hölder condition such that $H^{p(\cdot)}\neq H^q$ for any constant exponent $1<q<\infty$. We also consider the variable exponent version of the Hardy space on the upper-half plane.
We give three characterizations of the Dirichlet-type spaces $D(μ)$. First we characterize $D(μ)$ in terms of a double integral and in terms of the mean oscillation in the Bergman metric, none of them involve the use of derivatives. Next, we obtain another characterization for $D(μ)$ in terms of higher order derivatives. Also, a decomposition theorem for $D(μ)$ is established.
In this article we characterize the boundedness and compactness of a Toeplitz-type operator on weighted Bergman spaces satisfying the so-called Bekolle-Bonami condition in terms of the Berezin transform.