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Contributed Talks
W. AbuShammala - Indiana University |
Title: The Hardy-Lorentz spaces H^{p,q}(R^n)
Abstract
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P.
Avramidou - Ohio State University |
Title: Certain sequences of reals and convergence, recurrence
Abstract:
For a one-parameter continuous flow $\{S^t\}_{t\in\mathbb{R}}$, and sequences
$x_n=p(n)\lfloor q(n)\rfloor,\ n\in\mathbb{N}$, where $p,q$ are of the form
$\sum a_i x^{\alpha_i}$ we study the convergence (in norm,
pointwise) of the averages $\frac{1}{N} \sum_{n=1}^N f\circ S^{x_n}$. This
is closely related to the question of recurrence along the sequences
$\lfloor x_n \rfloor$ for discrete flows. This is a joint
work with V. Bergelson (Ohio State University),
I.J. Knutson (Agder University College, Norway) |
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L. DeCarli - Florida International
University |
Title: Reverse Holder inequalities for polynomials on (0,1)
Abstract: We prove new weighted reverse Holder inequalities for the classical
ultraspherical polynomials and, more in general, for polynomials on [0,1].
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C. Demeter - UCLA |
Title: Breaking the duality in the Return Times Theorem
Abstract:
Bourgain proved the following Return Times theorem:
Let ${\bf X}=(X,\Sigma,\mu, \tau)$ be a dynamical system.
Let also $1\le p,q\le \infty$ be such that $\frac1p+\frac1q\le 1$.
For each function $f\in L^{p}(X)$ there is a universal set $X_0\subseteq
X$ with $\mu(X_0)=1$, such that for each second dynamical system ${\bf
Y}=(Y,\F,\nu,\sigma)$, each $g\in L^{q}(Y)$ and each $x\in X_0$, the
averages
$$\frac1{N}\sum_{n=0}^{N-1}f(\tau^nx)g(\sigma^ny)$$
converge $\nu$- almost everywhere.
We show how to break the duality in this theorem. More precisely, we prove
that the result remains true if $p>1$ and $q\ge 2$. We emphasize the
strong connections between this result and the Carleson-Hunt theorem on
the convergence of the Fourier series. We also prove similar results for
the analog of Bourgain's theorem for series, where no positive
results were previously known.
This is joint work with Michael Lacey, Terence Tao and Christoph
Thiele.
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A.E. Gatto - DePaul University |
Title: Lipschitz Spaces and Calderon-Zygmund Operators associated to non-doublin
g measures Abstract: In the setting if a metric measure space (X,d,\mu) with an n-dimensional
Radon measure \mu, we give a necessary and sufficient condition for the boundedness
of CZ operators associated to the measure \mu on Lipschitz space on the support of \mu.
ALso, for the Eucleadean space R^d with an arbitrary Radon measure \mu, we give
several characterization of Liptschitz spaces on the support of \mu, Lip(\alpha, \mu) in terms of
mean oscillations involving \mu. This allows us to view the "regular" BMO space of X.Tolsa
as a limiting case for \alpha\to 0 of the space Lip(\alpha, \mu).
This is a joint work with Jose Garsia-Cuerva. |
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M. Kulshrestha - Anand Agricultural
University, Anand, India |
Title: Estimation of soil Temperatures By Harmonic Analysis
Abstract |
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T. Mei - Texas A&M University |
Title: Matrix (Operator) valued Hardy Spaces
Abstract:
We studied Hardy spaces for matrix valued functions(more
general, for functions with values in the non-commutative L^p spaces
with a semifinite von Neuman algebra). This is motivated by recent study
on matrix valued harmonic anlaysis and non-commutative martingale
inequalities. Besides several non-commutative analogues of classical
results, we proved our matrix valued H^1 is a predual of a matrix valued
BMO spaces raised from these two directions. Our matrix valued Hardy spaces are
defined by non-commutative Littlewood-Paley G-functions.
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Biao Ou - University of
Toledo |
Title: Radial Symmetry and Monotonicity of Positive Regular Solutions to
an Integral Equation
Abstract:
We use the method of moving planes to prove the
radial symmetry and monotonicity of positive regular solutions to the
integral equation
$$
u(x) = \int_{R^n} \frac{1}{ |x-y|^{n-\alpha} } u(y)^{(n+\alpha)/(n-\alpha) } dy
$$
where $0<\alpha< n$. It follows that the solutions are a constant
multiple of functions of form
$$(\frac{t}{t^2 + |x-x_{0}|^2})^{(n-\alpha)/2 }$$
where $ t>0, x_{0} \in R^n.$ This is a joint work with Wenxiong Chen and Congming Li.
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C. Rios - Trinity College |
Title: Harmonic measure for elliptic operators with singular drift
Abstract: Given two elliptic operators in nondivergence form with singular drift terms
in a Lipschitz domain, it is shown that if the difference of their
coefficients satisfy certain Carleson measure condition, then their
respective harmonic measures belong the same A_\infty class. This is an
analog result to known theory for divergence form operators. As an
application of this and a new approximation argument we are able to extend
known results for divergence form operators while obtaining totally new
theorems for nondivergence form operators. The theorems are sharp in all
cases.
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P. Roy - Cornell University |
Title: Hopf Decomposition of Nonsingular Z^d-Actions and
Long Range Dependence of Stationary S\alphaS Random Fields
Abstract: Jan Rosinski (2000) obtained a decomposition of a stationary
symmetric \alpha-stable random field into three independent parts.
This work establishes the connection between this decomposition and
Hopf decomposition of nonsingular Z^d-actions. With the
help of this connection, we study a partial maxima sequence of the
stable random field. Depending on the ergodic theoretical structures
of the underlying group action, we observe different kinds of
asymptotic behavior of this partial maxima sequence and argue that
this may indicate a phase transition from short memory to long
memory. This is a joint work with Gennady Samorodnitsky.
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G. Sampson - Auburn University |
Title: Mapping Properties for Oscillatory Integrals in d-Dimensions
Abstract |
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C. Silva - Williams College |
Title: Mixing Rank-One Actions of Locally Compact Abelian Groups Abstract |
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Yue Wu - Rice University |
Title: Whirly automorphisms
Abstract: Borel lift from a group action defined on the measure algebra to a
Borel action was recently studied by E. Glasner, B. Tsirelson, B.
Weiss. In the same paper, they defined "whirly action' and
showed that whirly action has no spatial factor. In my thesis, it
is proved that almost all three interval exchange
transformations(i.e.t.) with permutation (321) are whirly (with
respect to weak topology). The whirly property on all the cylinder
sets is also gained for del Junco-Rudolph's map.
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