Harmonic Analysis Komaba Seminar

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Date, time & place Saturday 13:00 - 18:00 128Room #128 (Graduate School of Math. Sci. Bldg.)

2015/05/02

13:30-17:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Hitoshi Tanaka (Univ Tokyo) 13:30-15:00
Two-weight Morrey norm inequality and the sequential testing
(日本語)
[ Abstract ]
In this talk we extend Sawyer's two-weight theory to Morrey spaces and give a characterization of two-weight Morrey norm inequalities for the (general) Hardy-Littlewood maximal operators in terms of the sequential testing due to H\"{a}nninen, Hyt\"{o}nen and Li.
We also introduce the description of the K\"othe dual of Morrey type spaces generated by a basis of measurable functions.
The second topic is based on a joint work with Professors Sawano (Tokyo Metropolitan University) and Masty{\l}o (Adam Mickiewicz University and Institute of Mathematics).
Yoshihiro Sawano (Tokyo Metropolitan University.) 15:30-17:00
The topology of the dual space of ${\mathcal S}_0$
(日本語)
[ Abstract ]
Based on the notation of my Japanese book, I will consider the topology of ${\mathcal S}_0'$, the dual of ${\mathcal S}_0$.
In view of the linear isomorphism ${\mathcal S}_0' \sim {\mathcal S}/{\mathcal P}$, we can consider two different topologies;

1) the weak-* topology
and
2) the quotient topology in ${\mathcal S}/{\mathcal P}$.

We aim to show that these two topologies are the same. This will be an errortum of my Japanese book.
This work is done jointly with Takahiro Noi and Shohei Nakamura in Tokyo Metropolitan University.