Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Littlewood-Paley formulas and Carleson measures for weighted Fock spaces
  induced by $A_\infty$-type weights   We obtain Littlewood-Paley formulas for Fock spaces
$\mathcal{F}^q_{\beta,\omega}$ induced by weights $\omega\in
A^{restricted}_\infty=\cup_{1\le p<\infty}A^{restricted}_{p}$, where
$A^{restricted}_{p}$ is the class of weights such that the Bergman projection
$P_\alpha$, on the classical Fock space $\mathcal{F}^2_{\alpha}$, is bounded on
  $$\mathcal{L}^p_{\alpha,\omega}:=\left\{f:\,
\int_{\mathbb{C}}|f(z)|^pe^{-p\frac{\alpha}{2}|z|^2}\,\omega(z)dA(z)<\infty
\right\}. $$
  Using these equivalent norms for $\mathcal{F}^q_{\beta,\omega}$ we
characterize the Carleson measures for weighted Fock-Sobolev spaces
$\mathcal{F}^{q,n}_{\beta,\omega}$.

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