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Eighth Prairie Analysis
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Bus Transportation in Lawrence
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Talks Titles and AbstractsEric SawyerWeighted inequalities for maximal singular integrals and applicationsWe discuss a recent characterization of two weight norm inequalities for maximal singular integrals (joint work with M. Lacey and I. Uriarte-Tuero) along with applications to distortion of Hausdorff measure by quasiconformal maps, boundedness of Cauchy type kernels, and function theory. We will discuss certain problems of harmonic analysis that employ methods of analytic number theory.
Xiaochun LiBilinear Hilbert transforms along curvesWe establish an $L^2 x L^2 to L^1$ estimate for the bilinear Hilbert transform along a polynomial curve. Our proof is closely related to multilinear oscillatory integrals and "quadratic" Fourier analysis. Extended Abstract (pdf file)
Carlos PérezSharp weighted bound for Calderón-Zygmund singular integral operators and Sobolev inequalitiesIn the first part of this talk we will present some recent results about a sharp weighted weak type $(1,1)$ estimate for any Calderón-Zygmund singular integral operator assuming that the weight satisfy the $A_1$ condition. This result is related to a problem of Muckenhoupt-Wheeden that we will discuss. We will show that the endpoint result follows by proving first a corresponding sharp weighted $L^p$ estimate both sharp on $p$ and the $A_1$ constant of the weight. The connection of this result with the $A_2$ conjecture for Singular Integrals Operators will be discussed as well. In the second part, we will show some sharp strong type weighted estimates for Sobolev type inequalities. They will be derived from corresponding weak type results for fractional integrals. The proof is based on a sharp off-diagonal extrapolation theorem and an appropriate discretization of the fractional integrals. The first part of the lecture is based on a joint work with A. Lerner and S. Ombrosi and the second on joint work with K. Moen and R. Torres.
Contributed Talks
Organizers:Estela A. Gavosto, KUMarianne Korten, KSU Charles Moore, KSU Rodolfo H. Torres, KU |
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