We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to i...We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions.展开更多
We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for ...We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for the case wherein the particles have a positive probability of having no children. Then using this tool, we obtain results regarding the asymptotic behavior of the number of particles above λt at time t for λ>0. Under an L log L condition, we prove a strong law of large numbers for this catalytic branching Brownian motion.展开更多
文摘We introduce a new function space that is much finer than the classical Lebesgue spaces, and investigate the continuity and the discontinuity of the Calderon-Zygmund operators on the new weighted spaces. In order to identify the continuity of singular integrals, we prove an interpolation theorem on the new spaces and propose a concept of the spectrum of base functions.
基金supported by National Natural Science Foundation of China (Grant No. 10871011)
文摘We consider a catalytic branching Brownian motion with general branching which takes place only when particles are at the origin at a rate β>0 on the local time scale. We first establish a spine decomposition for the case wherein the particles have a positive probability of having no children. Then using this tool, we obtain results regarding the asymptotic behavior of the number of particles above λt at time t for λ>0. Under an L log L condition, we prove a strong law of large numbers for this catalytic branching Brownian motion.
