Function spaces of parabolic Bloch type
Hishikawa, Yôsuke ; Yamada, Masahiro
Hiroshima Math. J., Tome 41 (2011) no. 1, p. 55-87 / Harvested from Project Euclid
The $L^{(\alpha)}$-harmonic function is the solution of the parabolic operator $L^{(\alpha)}= \partial_{t}+(-\Delta_{x})^{\alpha}$. We study a function space $\widetilde{{\cal B}}_{\alpha}(\sigma)$ consisting of $L^{(\alpha)}$-harmonic functions of parabolic Bloch type. In particular, we give a reproducing formula for functions in $\widetilde{{\cal B}}_{\alpha}(\sigma)$. Furthermore, we study the fractional calculus on $\widetilde{{\cal B}}_{\alpha}(\sigma)$. As an application, we also give a reproducing formula with fractional orders for functions in $\widetilde{{\cal B}}_{\alpha}(\sigma)$. Moreover, we investigate the dual and pre-dual spaces of function spaces of parabolic Bloch type.
Publié le : 2011-03-15
Classification:  Bloch space,  parabolic operator of fractional order,  reproducing formula,  35K05,  31B10,  32A18
@article{1301586290,
     author = {Hishikawa, Y\^osuke and Yamada, Masahiro},
     title = {Function spaces of parabolic Bloch type},
     journal = {Hiroshima Math. J.},
     volume = {41},
     number = {1},
     year = {2011},
     pages = { 55-87},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1301586290}
}
Hishikawa, Yôsuke; Yamada, Masahiro. Function spaces of parabolic Bloch type. Hiroshima Math. J., Tome 41 (2011) no. 1, pp.  55-87. http://gdmltest.u-ga.fr/item/1301586290/