Boundary value representations for bounded hyperfunctions and some variants (Recent development of microlocal analysis and asymptotic analysis)
Yasunori Okada · Kyoto University Research Information Repository (Kyoto University) · 2013
There are two notions of boundedness for hyperfunctions: the space $\mathcal{B}_{L}\infty$ of bounded hyperfunctions and the sheaf $\mathscr{B}_{L}\infty$ of bounded hyperfunctions at infinity.The former was introduced by Chung-Kim-Lee [2] using a duality method, and the latter was introduced by [5] in a cohomological manner, where we also gave an identification between $\mathcal{B}_{L}\infty$ in one dimensional case and the space of the global sections of $\mathscr{B}_{L}\infty$ .This identification can be regarded as boundary value representations of bounded hyperfunctions in one dimensional case.In this report, we study bounded hyperfunctions in the general case, and announce our recent result on their boundary value representations by bounded holomorphic functions on wedges with respect to the octant decompositions.We also mention some variants including reflexive-valued cases.