Radonification of cylindrical semimartingales on Hilbert spaces

Albert Badrikian; Ali Süleyman Üstünel

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We extend some recent work of S. Y. Chang, J. M. Wilson and T. Wolff to the bidisc. For $f \in L_{l o c}^{1} (R^{2})$ , we determine the sharp order of local integrability obtained when the square function of $f$ is in $L^{\infty}$ . The Calderón-Torchinsky decomposition reduces the problem to the case of double dyadic martingales. Here we prove a vector-valued form of an inequality for dyadic martingales that yields the sharp dependence on p of $C_{p}$ in $∥ f ∥_{p} \leq C_{p} ∥ S f ∥_{p}$ .

Large deviation estimate of transition densities for jump processes

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