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Elliptic and parabolic integro-differential model problems are considered inthe whole space. By verifying H\"ormander condition, the existence anduniqueness is proved in L_{p}-spaces of functions whose regularity is definedby a scalable, possibly nonsymmetric, Levy measure. Some rough probabilitydensity function estimates of the associated Levy process are used as well.

On Lp -theory for parabolic and elliptic integro-differential equations with scalable operators in the whole space