Fock-Sobolev spaces and their Carleson measures

By Hong-Rae Cho, Kehe Zhu. 2012

134 citations recorded by the source corpus.

We consider the Fock-Sobolev space $F^{p,m}$ consisting of entire functions $f$ such that $f^{(m)}$, the $m$-th order derivative of $f$, is in the Fock space $F^p$. We show that an entire function $f$ is in $F^{p,m}$ if and only if the function $z^mf(z)$ is in $F^p$. We also characterize the Carleson measures for the spaces $F^{p,m}$, establish the boundedness of the weighted Fock projection on appropriate $L^p$ spaces, identify the Banach dual of $F^{p,m}$, and compute the complex interpolation space between two $F^{p,m}$ spaces.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/aa3a0c1285910a2745a7da7ebdc5d6dabb97dae6

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In Applied Mathematics

1. J. A. Pel'aez
2. O. Constantin
3. Jouni Rattya
4. Jordi Pau

In Geometry and Topology

1. O. Constantin
2. J. A. Pel'aez
3. Jouni Rattya

Citations in the corpus

• Integral Operators, Embedding Theorems and a Littlewood–Paley Formula on Weighted Fock Spaces (2013, background): “INTEGRAL OPERATORS ON WEIGHTED FOCK SPACES 3 This problem was studied in [9, 10, 18] for the classical Fock space.”