Heat kernels for time-dependent non-symmetric stable-like operators

2017/09/14 by Chen, Zhen-Qing, Zhang, Xicheng
#47G20 #60J35 #FOS: Mathematics #Primary 35K05 #Probability (math.PR) #Secondary 47D07

paper · doi:10.48550/arxiv.1709.04614

Abstract

When studying non-symmetric nonlocal operators \cal L f(x) = ∫_\bf R^d ( f(x+z)-f(x)-∇ f(x)⋅ z 1_\|z|≤ 1\ ) \fracκ(x, z)|z|^d+α d z , where 02d/(d+2α), ‖ \cal L^1/2f‖_p\asymp ‖Γ(f)^1/2‖_p, where Γ(f):=(1)/(2)\cal L (f²)-f \cal L f is the carré du champ operator associated with \cal L, and \cal L^1/2 is the square root operator of \cal L defined by using Bochner's subordination. Here \asymp means that both sides are comparable up to a constant multiple.

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