Monday Analysis Seminar: Atomic decomposition and interpolating seqences for parabplic Bergman spaces

2011-12-5 14:45 - 2011-12-5 16:15
Faculty of Science Buliding #3 Room 210
Masaharu Nishio (Osaka City University)
We consider  a parabolic equation
$(\partial/\partial t + (-\Delta_x)^\alpha)u = 0$
on the upper half space
$R^{n+1}_+ = \{(x,t)|x\in R^n, t>0\}$
and denote by  $b^p_\alpha$ the space of all $L^p$-solutions,
where $0 < \alpha \leq 1$.
We call  $b^p_\alpha$ the parabolic Bergman space.

In the present talk, using $\alpha$-parabolic dilations,
which preserve the equation, we explain

  • The $L^p$-boundedness of Bergman projections,

  • the atomic decompositions of Bergman functions,

  • interpolating seqences for Bergman spaces.