Probabilistic Behavior of Harmonic Functions

Aau(x Alu(x analogue apply Green's theorem area integral Bañuelos Bloch functions Brossard Brownian motion Burkholder C.N. Moore C1 and C2 C₁ exp C₂ Calderón caloric functions Cauchy-Riemann equations Chapter completes the proof cone consider constants C1 Dau(x define denote density depending Dhu(x Dirichlet problem dsdt Du(x Dwu(x dyadic martingales exists a constant Fefferman follows good-A inequalities Green's theorem Hardcover harmonic functions implies ISBN iterated logarithm K₁ Key Estimate L¹(R lacunary series Lebesgue measure LIL's lim sup lim sup P↑1 Lipschitz constant Lipschitz domains log log Lusin area function Marcinkiewicz martingale measure Nau(x nontangential limit nontangential maximal function notation Note numbers obtain Poisson kernel proof of Lemma proof of Theorem Proposition prove R+¹ random variables result Riesz satisfies sidelength square function Suppose Vu(s zero Zygmund ди