Littlewood–Paley–Stein functions for non-local Schrödinger operators

Motivated by recent works on vertical Littlewood–Paley–Stein functions for symmetric non-local Dirichlet forms and local Schrödinger type operators respectively, we study Littlewood–Paley–Stein functions for non-local Schrödinger type operators with non-negative potential in metric measure spaces. W...

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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2020-11, Vol.24 (5), p.1293-1312
Main Authors: Li, Huaiqian, Wang, Jian
Format: Article
Language:English
Subjects:
Calculus of Variations and Optimal Control
Optimization
Dirichlet problem
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Operators (mathematics)
Potential Theory
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Summary:Motivated by recent works on vertical Littlewood–Paley–Stein functions for symmetric non-local Dirichlet forms and local Schrödinger type operators respectively, we study Littlewood–Paley–Stein functions for non-local Schrödinger type operators with non-negative potential in metric measure spaces. We prove the L p -boundedness of Littlewood–Paley–Stein functions for all p ∈ ( 1 , 2 ] , and further find that the L p -boundedness for some p ∈ ( 2 , ∞ ) implies the vanishment of a particular class of potentials.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-019-00733-w