On L^p-(un)boundedness of Szegö projections

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• Gian Maria Dall'Ara (Birmingham)
• Tuesday 01 October 2019, 14:00-15:00
• Watson 310.

If you have a question about this talk, please contact Alessio Martini.

The Szegö projection of a domain Ω in Cⁿ is the orthogonal projection S : L²(bΩ) → L²(bΩ) onto the subspace of boundary values of holomorphic functions in Ω. Starting with the pioneering work of Folland and Stein in the 1970s, harmonic analysts understood that Szegö projections are not only of interest in the function theory of several complex variables, but also as natural examples of singular integral operators lying beyond the scope of the classical Calderón–Zygmund theory.

In my talk I will rapidly review known facts about Lp-(un)boundedness of Szegö projections and present new results I obtained recently, focusing on behaviour on L¹ and obstructions to L^p-boundedness for p ≠ 2. The latter extend in particular a very recent work of Lanzani and Stein [1].

References

[1] L. Lanzani and E.M. Stein, On regularity and irregularity of certain holomorphic singular integral operators, arXiv:1901.03402.

This talk is part of the Analysis Seminar series.

This talk is included in these lists:

• Analysis Seminar
• School of Mathematics Events
• Watson 310

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