Seminars and Colloquia by Series

Lp theory for outer measures

Series
Analysis Seminar
Time
Wednesday, May 1, 2013 - 10:07 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yen Do – Yale University
In this talk I will describe an Lp theory for outer measures, which could be used to connect two themes of Lennart Carleson's work: Carleson measures and time frequency analysis. This is joint work with Christoph Thiele.

Operator theory from several complex variables perspective

Series
Analysis Seminar
Time
Wednesday, April 3, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Sonmez Sahutoglu – University of Toledo
Complex analysis in several variables is very different from the one variable theory. Hence it is natural to expect that operator theory on Bergman spaces of pseudoconvex domains in $\mathbb{C}^n$ will be different from the one on the Bergman space on the unit disk. In this talk I will present several results that highlight this difference about compactness of Hankel operators. This is joint work with Mehmet Celik and Zeljko Cuckovic.

Wolff's Ideal Problem in the Multiplier Algebra on weighted Dirichlet Space

Series
Analysis Seminar
Time
Wednesday, March 27, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Debendra Banjade – University of Alabama
In 1980, T. M. Wolff has given the following version of the ideal membership for finitely generated ideals in $H^{\infty}(\mathbb{D})$: \[\ensuremath{\mbox{If \,\,}\left\{ f_{j}\right\} _{j=1}^{n}}\subset H^{\infty}(\mathbb{D}),\, h\in H^{\infty}(\mathbb{D})\,\,\mbox{and }\]\[\vert h(z)\vert\leq\left(\underset{j=1}{\overset{n}{\sum}}\vert f_{j}(z)\vert^{2}\right)^{\frac{1}{2}}\,\mbox{for all \ensuremath{z\in\mathbb{D},}}\]then \[h^{3}\in\mathcal{I}\left(\left\{ f_{j}\right\} _{j=1}^{n}\right),\,\,\mbox{the ideal generated by \ensuremath{\left\{ f_{j}\right\} _{j=1}^{n}}in \ensuremath{H^{\infty}}\ensuremath{(\mathbb{D})}. }\]In this talk, we will give an analogue of the Wolff's ideal problem in the multiplier algebra on weighted Dirichlet space. Also, we will give a characterization for radical ideal membership.

Estimates of the Discrepancy Function in Exponential Orlicz Spaces

Series
Analysis Seminar
Time
Wednesday, March 13, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Gagik Amirkhanyan – Georgia Tech
For dimensions n greater than or equal to 3, and integers N greater than 1, there is a distribution of points P in a unit cube [0,1]^{n}, of cardinality N, for which the discrepancy function D_N associated with P has an optimal Exponential Orlicz norm. In particular the same distribution will have optimal L^p norms, for 1 < p < \infty. The collection P is a random digit shift of the examples of W.L. Chen and M. Skriganov.

The Spectrum and Essential Spectrum of Toeplitz Operators

Series
Analysis Seminar
Time
Wednesday, March 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dechao Zheng – Vanderbilt University
On the Hardy space, by means of an elegant and ingenious argument, Widom showed that the spectrum of a bounded Toeplitz operator is always connected and Douglas showed that the essential spectrum of a bounded Toeplitz operator is also connected. On the Bergman space, in 1979, G. McDonald and the C. Sundberg showed that the essential spectrum of a Toeplitz operator with bounded harmonic symbol is connected if the symbol is either real or piecewise continuous on the boundary. They asked whether the essential spectrum of a Toeplitz operator on the Bergman space with bounded harmonic symbol is connected. In this talk, we will show an example that the spectrum and the essential spectrum of a Toeplitz operator with bounded harmonic symbol is disconnected. This is a joint work with Carl Sundberg.

The A_2 Theorem for spaces of homogeneous type

Series
Analysis Seminar
Time
Wednesday, February 27, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Theresa Anderson – Brown University
A recent conjecture in harmonic analysis that was exploredin the past 20 years was the A_2 conjecture, that is the sharp bound onthe A_p weight characteristic of a Calderon-Zygmund singular integraloperator on weighted L_p space. The non-sharp bound had been knownsince the 1970's, but interest in the sharpness was spurred recentlyby connections to quasiconformal mappings and PDE. Finally solved infull by Hytonen, the proof is complex, intricate and lengthy. A new "simple" approach using local mean oscillation and positive operatorbounds was published by Lerner. We discuss this and some recent progress in the area, including our new proof for spaces of homogeneoustype, in the style of Lerner (Joint work with Armen Vagharshakyan).

The Essential Norm of Operators on the Bergman Space.

Series
Analysis Seminar
Time
Wednesday, February 20, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Brett Wick – Georgia Tech
In this talk, we will characterize the compact operators on Bergman spaces of the ball and polydisc. The main result we will discuss shows that an operator on the Bergman space is compact if and only if its Berezin transform vanishes on the boundary and additionally this operator belongs to the Toeplitz algebra. We additionally will comment about how to extend these results to bounded symmetric domains, and for "Bergman-type" function spaces.

One sided bump conditions and two weight boundedness of Calderon-Zygmund operators

Series
Analysis Seminar
Time
Wednesday, February 6, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Alexander Reznikov – Michigan State University
We consider a so-called "One sided bump conjecture", which gives asufficient condition for two weight boundedness of a Calderon-Zygmundoperator. The proof will essentially use the Corona decomposition, which isa main tool for a first proof of $A_2$ (also, $A_p$ and $A_p-A_\infty$)conjecture. We will focus on main difficulty, that does not allow to get afull proof of our one sided bump conjecture.

One and Two Weight Theory in Harmonic Analysis

Series
Analysis Seminar
Time
Wednesday, January 30, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
James Scurry – Georgia Tech
We will study one and two weight inequalities for several different operators from harmonic analysis, with an emphasis on vector-valued operators. A large portion of current research in the area of one weight inequalities is devoted to estimating a given operators' norm in terms of a weight's A_p characteristic; we consider some related problems and the extension of several results to the vector-valued setting. In the two weight setting we consider some of the difficulties of characterizing a two weight inequality through Sawyer-type testing conditions.

Boundedness of matrix valued dyadic paraproducts on matrix weighted L^p

Series
Analysis Seminar
Time
Wednesday, January 16, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josh Isralowitz – SUNY Albany
Weighted norm inequalities for singular integral operators acting on scalar weighted L^p is a classical topic that goes back to the 70's with the seminal work of R. Hunt, B. Muckenhoupt, and R. Wheeden. On the other hand, weighted norm inequalities for singular integral operators with matrix valued kernels acting on matrix weighted L^p are poorly understood and results (obtained by F. Nazarov, S. Treil, and A. Volberg in the late 90's) are only known for the situation when the kernel is essentially scalar valued.In this talk, we discuss matrix weighted norm inequalities for matrix valued dyadic paraproducts and discuss the possibility of using our results and a recent result of T. Hytonen to obtain concrete weighted norm inequalities for singular integral operators with matrix kernels acting on matrix weighted L^p. This is joint work with Hyun-Kyoung Kwon and Sandra Pott.

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