• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.119-142
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• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1009-1031
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• 2013

In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica [5], our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.713-725
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• 1998

Let X and Y be Ito processes with dX$_{s}$ = $\phi$$_{s}$dB$_{s}$ ＋ $\psi$$_{s}$ds and dY$_{s}$ = (equation omitted)dB$_{s}$ ＋ ξ$_{s}$ds. Burkholder obtained a sharp bound on the distribution of the maximal function of Y under the assumption that │Y$_{0}$│$\leq$│X$_{0}$│,│ζ│$\leq$│$\phi$│, │ξ│$\leq$│$\psi$│ and that X is a nonnegative local submartingale. In this paper we consider a wider class of Ito processes, replace the assumption │ξ│$\leq$│$\psi$│ by a more general one │ξ│$\leq$$\alpha$ │$\psi$│ , where a $\geq$ 0 is a constant, and get a weak-type inequality between X and the maximal function of Y. This inequality, being sharp for all a $\geq$ 0, extends the work by Burkholder.der.urkholder.der.