Littlewood-Paley formulas and Carleson measures for weighted Fock spaces\n induced by A_\∞-type weights

2016/12/22 by Carme Cascante, Cascante, Carme, Joan Fàbrega +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1612.07458

openalex publication_date 2016/12/22 · openalex created_date 2022/09/20 · openalex updated_date 2026/07/28

Abstract

We obtain Littlewood-Paley formulas for Fock spaces\n\F^q_\β,\ω induced by weights \ω\∈\nA^restricted_\∞=\∪_{1\≤ p<\∞}A^restricted_p, where\nA^restricted_p is the class of weights such that the Bergman projection\nP_\α, on the classical Fock space \F²_\α, is bounded on\n
mathcalL^p
_alpha,
omega:=
left
f:
,\n
int_
mathbbC|f(z)|^pe^-p
frac
alpha2|z|²
,
omega(z)dA(z)lt;
infty\n
right
.\n Using these equivalent norms for \F^q_\β,\ω we\ncharacterize the Carleson measures for weighted Fock-Sobolev spaces\n\F^q,n_\β,\ω.\n

Related

• Carleson type measures for Fock--Sobolev spaces
• Integral operators, embedding theorems and a Littlewood-Paley formula on\n weighted Fock spaces
• Fock projections on vector-valued L^p-spaces with matrix weights
• Carleson measures for weighted Hardy-Sobolev spaces
• Sharp weighted norm inequalities for Littlewood-Paley operators and\n singular integrals