Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion |
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Authors: | Email author" target="_blank">Deniz?Karl?Email author |
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Institution: | 1.Department of Mathematics,The University of British Columbia,Vancouver,Canada |
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Abstract: | In this paper, we consider a product of a symmetric stable process in ? d and a one-dimensional Brownian motion in ??+?. Then we define a class of harmonic functions with respect to this product process. We show that bounded non-negative harmonic functions in the upper-half space satisfy Harnack inequality and prove that they are locally Hölder continuous. We also argue a result on Littlewood–Paley functions which are obtained by the α-harmonic extension of an L p (? d ) function. |
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