Schedule of Spring/Summer School: Carleson theorems and Radon type behaviour

Monday, May 26

08:45 - 09:30 Shaoming Guo: Singular and Maximal Radon Transform: Analysis and Geometry - Part I
09:45 - 10:30 Joris Roos: Singular and maximal Radon transforms: analysis and geometry. Part 2
10:30 - 11:00 Coffee break
11:00 - 11:45 Yumeng Ou: Lp theory for outer measures
11:45 - 13:15 Lunch break
13:15 - 14:00 Polona Durcik: Lp theory for outer measures and two themes of Lennart Carleson united (Part 2)
14:00 - 14:45 Ioann Vasilyev: Extention of a multi-frequency maximal inequality of Bourgain
15:00 - 16:00 Senior lecture - Tuomas Hytönen: Recent advances on weighted estimates in harmonic analysis
16:00 - 16:30 Tea and cake
16:30 - 17:15 Luis Daniel Lopez-Sanchez: Uniform bounds for a Walsh model of the bilinear Hilbert transform

Tuesday, May 27

08:45 - 09:30 Guillermo Rey: A proof of boundedness of the Carleson operator
09:45 - 10:30 Kevin Hughes: Single Annulus Lp Estimates for Hilbert Transforms along Vector Fields
10:30 - 11:00 Coffee break
11:00 - 11:45 Cristina Benea: Lp Estimates for the Hilbert Transform along a one-variable Vector Field
11:45 - 13:15 Lunch break
13:15 - 14:00 Prince Romeo Mensah: Weak-type (1 ; 1) bounds for oscillatory singular integrals with rational phases
14:00 - 14:45 Jose M. Conde-Alonso: Oscillatory integrals related to Carleson's theorem
15:00 - 16:00 Senior lecture - Detlef Müller: On Lp -multipliers for subelliptic operators
16:00 - 16:30 Tea and cake
16:30 - 17:15 Theresa C. Anderson: A polynomial Carleson operator along the paraboloid

Thursday, May 29

08:45 - 09:30 Gennady Uraltsev: The (weak- L2) boundedness of the quadratic Carleson operator
09:45 - 10:30 (EG) Shaoming Guo: Singular and Maximal Radon Transform: Analysis and Geometry - Part I
09:45 - 10:30 (UG) Yumeng Ou: Lp theory for outer measures
10:30 - 11:00 Coffee break
11:00 - 11:45 (EG) Joris Roos: Singular and maximal Radon transforms: analysis and geometry. Part 2
11:00 - 11:45 (UG) Polona Durcik: Lp theory for outer measures and two themes of Lennart Carleson united (Part 2)
11:45 - 13:15 Lunch break
13:15 - 14:00 (EG) Ioann Vasilyev: Extention of a multi-frequency maximal inequality of Bourgain
13:15 - 14:00 (UG) Kevin Hughes: Single Annulus Lp Estimates for Hilbert Transforms along Vector Fields
14:00 - 14:45 (EG) Luis Daniel Lopez-Sanchez: Uniform bounds for a Walsh model of the bilinear Hilbert transform
14:00 - 14:45 (UG) Cristina Benea: Lp Estimates for the Hilbert Transform along a one-variable Vector Field
15:00 - 16:00 Senior lecture - Stefan Buschenhenke: A Fourier restriction estimate for a surface of finite type
16:00 - 16:30 Tea and cake
16:30 - 17:15 (EG) Guillermo Rey: A proof of boundedness of the Carleson operator
16:30 - 17:15 (UG) Prince Romeo Mensah: Weak-type (1 ; 1) bounds for oscillatory singular integrals with rational phases

Abstracts

Theresa C. Anderson: A polynomial Carleson operator along the paraboloid

We prove an Lp bound for a polynomial Carleson operator integrated along a parabolloid. This integration introduces Radon-type behavior which leads to new innovation in the techniques and style of proof.

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Cristina Benea: L^p Estimates for the Hilbert Transform along a one-variable Vector Field

Boundedness of the Hilbert transform along a non-vanishing vector field was proved in [2], under the assumptions that the vector fi eld only depends on one variable and 2/3 < p < ∞. Here we present the main ideas of the proof.

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Jose M. Conde-Alonso: Oscillatory integrals related to Carleson's theorem

The authors of [3] prove an (almost) generalization of the famous Carleson theorem on oscillatory integrals of the second kind, hence initiating the study of variants of the Carleson operator. We summarize their results.

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Polona Durcik: L^p theory for outer measures and two themes of Lennart Carleson united (Part 2)

We discuss an application of outer Lp spaces in time-frequency analysis. Using a generalized Carleson embedding theorem we reprove bounds for the bilinear Hilbert transform.

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Luis Daniel Lopez-Sanchez: Uniform bounds for a Walsh model of the bilinear Hilbert transform

We study the Lp boundedness behaviour of Walsh analogues of bilinear Hilbert transforms at the known region of exponents and beyond. The main tool at our disposal for exponents close to 1 is a multi-frequency Calderon-Zygmund decomposition.

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Prince Romeo Mensah: Weak-type (1 ; 1) bounds for oscillatory singular integrals with rational phases

This paper considers singular integral operators on R with an oscillatory factor that has a rational phase R(x) = P(x) = Q(x). Relying only on the degrees of P and Q, the paper derives weak-type (1 ; 1) bounds for such operators and establishes conditions for which these operators map the Hardy norm H1 into itself or into L1.

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Yumeng Ou: L^p theory for outer measures

We develop a theory of Lp spaces based on outer measures, which includes as a special case the classical Lp theory on Euclidean spaces. As an application, we rephrase several classical results concerning Carleson embedding, paraproducts and the T(1) theorem in the language of outer measure spaces.

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Guillermo Rey: A proof of boundedness of the Carleson operator

We give a short summary of the proof of the weak-type (2,2) boundedness of the Carleson operator in [5].

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Joris Roos: Singular and maximal Radon transforms: analysis and geometry. Part 2

The authors of [1] show Lp boundedness of a class of singular Radon transforms and their corresponding maximal operators under some curvature assumption. This condition can be formulated in essentially three di erent ways which are all equivalent.

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Bartosz Trojan: On maximal ergodic theorem for certain subsets of the integers

We prove L2-boundedness of a maximal function for averages along the squares (n2 : n ∈ N).

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Gennady Uraltsev: The (weak- L 2 ) boundedness of the quadratic Carleson operator

[1] provides a proof of weak L2 boundedness of the Carleson operator with both linear and quadratic modulation terms. The proof is similar to [3] and it extends the time-frequency tile approach to be able to study the quadratic Carleson operator in terms of its vaster space of symmetries.

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Ioann Vasilyev: Extention of a multi-frequency maximal inequality of Bourgain

We give a proof of a strenghtened version of Bourgain's multi-frequency maximal inequality. Proof contains one nice version of Calderon-Zygmund decomposition.

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Michal Warchalski: Cotlar's ergodic theorem along the prime numbers

We prove Cotlar's ergodic theorem modeled on the set of primes.

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Pavel Zorin-Kranich: Pointwise ergodic theorems for arithmetic sets

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