An lp-boundedness of stochastic singular integral operators and its application to spdes

2016/08/31 by Kim, Ildoo, Kim, Kyeonghun
#35B45 #35S10 #42B20 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1608.08728

Abstract

In this article we introduce a stochastic counterpart of the Hörmander condtion on the kernel K(r,t,x,y): there exists a pseudo-metric ρ on (0,∞)× R^d and a positive constant C₀ such that for X=(t,x), Y=(s,y), Z=(r,z) ∈ (0,∞) × R^d, sup_X,Y∫₀^∞ [ ∫_{ρ(X,Z) ≥ C0 ρ(X,Y)} | K(r,t, z,x) - K(r,s, z,y)| ~dz]² dr

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