Banach June 2016

banach@mathdept.okstate.edu

1 participants
2 discussions

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu), so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Jan Rozendaal and Mark Veraar
by Bentuo Zheng (bzheng) 01 Jun '16

01 Jun '16

This is an announcement for the paper “Fourier multiplier theorems involving type and cotype” by Jan Rozendaal and Mark Veraar. Abstract: In this paper we develop the theory of Fourier multiplier operators $T_{m}:L^{p}(\mathbb{R}^{d};X)\to L^{q}(\mathbb{R}^{d};Y)$, for Banach spaces $X$ and $Y$, $1\leq p\leq q\leq \infty$ and $m:\mathbb{R}^{d}\to\mathcal{L}(X,Y)$ an operator-valued symbol. The case $p=q$ has been studied extensively since the 1980's and is reasonably well-understood. Far less is known for $p<q$. In the scalar case one can deduce results for $p<q$ from the case $p=q$ and additional arguments such as interpolation and Sobolev embedding techniques. However, in the vector-valued case this leads to restrictions both on the smoothness of the multiplier and the class of Banach spaces. For example, one often needs that $X$ and $Y$ are UMD spaces, and that $m$ satisfies a smoothness condition. For $p<q$ it turns out that the notions of type and cotype and other geometric conditions on $X$ and $Y$ are important to study Fourier multipliers. Moreover, we obtain boundedness results for $T_{m}$ without any smoothness properties of $m$. Under additional smoothness conditions we show that boundedness results can be extrapolated to other values of $p$ and $q$ as long as $\tfrac{1}{p}-\tfrac{1}{q}$ remains constant. Here we even extend classical results in the scalar case. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1605.09340

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Banach June 2016