In this paper we prove a parabolic version of the Littlewood-Paley inequality (1.4) for the operators of the type φ( - δ), where φ is a Bernstein function. As an application, we construct an L p-theory for the stochastic integro-differential equations of the type d u = ( - φ( - δ)u + f)d t + gdW t.
- Estimates of transition functions
- Integro-differential operators
- Lévy processes
- Parabolic Littlewood-Paley inequality
- Stochastic partial differential equations
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