%0 Journal Article %1 byczkowski2009bessel %A Byczkowski, T. %A Małecki, J. %A Ryznar, M. %D 2009 %J Trans. Amer. Math. Soc. %K Green_function potential_theory stable_processes %N 9 %P 4871--4900 %R 10.1090/S0002-9947-09-04657-1 %T Bessel potentials, hitting distributions and Green functions %U http://dx.doi.org/10.1090/S0002-9947-09-04657-1 %V 361 %X The purpose of the paper is to find explicit formulas for basic objects pertaining to the potential theory of the operator $ (I-\Delta)^\alpha/2$, which is based on Bessel potentials $ J_\alpha=(I-\Delta)^-\alpha/2$, $ 0<\alpha<2$. We compute the harmonic measure of the half-space and obtain a concise form for the corresponding Green function of the operator $ (I-\Delta)^\alpha/2$. As an application we provide sharp estimates for the Green function of the half-space for the relativistic process.

@article{byczkowski2009bessel, abstract = {The purpose of the paper is to find explicit formulas for basic objects pertaining to the potential theory of the operator $ (I-\Delta)^{\alpha/2}$, which is based on Bessel potentials $ J_{\alpha}=(I-\Delta)^{-\alpha/2}$, $ 0<\alpha<2$. We compute the harmonic measure of the half-space and obtain a concise form for the corresponding Green function of the operator $ (I-\Delta)^{\alpha/2}$. As an application we provide sharp estimates for the Green function of the half-space for the relativistic process. }, added-at = {2012-08-30T08:05:36.000+0200}, author = {Byczkowski, T. and Ma{\l}ecki, J. and Ryznar, M.}, biburl = {https://www.bibsonomy.org/bibtex/22853fc275444e7367d97e840cb3bf6bb/peter.ralph}, coden = {TAMTAM}, description = {MR: Publications results for "MR Number=(2506430)"}, doi = {10.1090/S0002-9947-09-04657-1}, fjournal = {Transactions of the American Mathematical Society}, interhash = {c485c52d503aa81a89a92fb878b737aa}, intrahash = {2853fc275444e7367d97e840cb3bf6bb}, issn = {0002-9947}, journal = {Trans. Amer. Math. Soc.}, keywords = {Green_function potential_theory stable_processes}, mrclass = {60J60 (31B15 60G52 60J65)}, mrnumber = {2506430 (2010m:60265)}, mrreviewer = {Yanxia Ren}, number = 9, pages = {4871--4900}, timestamp = {2012-08-30T08:05:36.000+0200}, title = {Bessel potentials, hitting distributions and {G}reen functions}, url = {http://dx.doi.org/10.1090/S0002-9947-09-04657-1}, volume = 361, year = 2009 }