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- Title
Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces.
- Authors
Cao, Guangfu; He, Li; Li, Ji; Shen, Minxing
- Abstract
We provide a boundedness criterion for the integral operator S φ on the fractional Fock–Sobolev space F s , 2 (C n) , s ≥ 0 , where S φ (introduced by Zhu [18]) is given by S φ F (z) : = ∫ C n F (w) e z · w ¯ φ (z - w ¯) d λ (w) with φ in the Fock space F 2 (C n) and d λ (w) : = π - n e - | w | 2 d w the Gaussian measure on the complex space C n . This extends the recent result in Cao et al. (Adv Math 363: 107001, 33 pp, 2020). The main approach is to develop multipliers on the fractional Hermite–Sobolev space W H s , 2 (R n) .
- Subjects
FRACTIONAL integrals; INTEGRAL operators; GAUSSIAN measures; FOCK spaces
- Publication
Mathematische Zeitschrift, 2022, Vol 301, Issue 4, p3671
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-022-03050-3