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CATEGORIES:Analysis Seminar
SUMMARY:On L^p-(un)boundedness of Szegö projections - Gian
Maria Dall'Ara (Birmingham)
DTSTART:20191001T130000Z
DTEND:20191001T140000Z
UID:TALK3871AT
URL:/talk/index/3871
DESCRIPTION:The Szegö projection of a domain Ω in C^n^ is the
orthogonal projection S : L^2^(bΩ) -> L^2^(bΩ) ont
o the subspace of boundary values of holomorphic f
unctions in Ω. Starting with the pioneering work o
f Folland and Stein in the 1970s\, harmonic analys
ts understood that Szegö projections are not only
of interest in the function theory of several comp
lex variables\, but also as natural examples of si
ngular integral operators lying beyond the scope o
f the classical Calderón–Zygmund theory.\n\nIn my
talk I will rapidly review known facts about Lp-(u
n)boundedness of Szegö projections and present new
results I obtained recently\, focusing on behavio
ur on L^1^ and obstructions to L^p^-boundedness fo
r p ≠ 2. The latter extend in particular a very re
cent work of Lanzani and Stein [1].\n\nReferences\
n\n[1] L. Lanzani and E.M. Stein\, _On regularity
and irregularity of certain holomorphic singular i
ntegral operators_\, arXiv:1901.03402.
LOCATION:Watson 310
CONTACT:Alessio Martini
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