ΠΑΝΕΠΙΣΤΗΜΙΟ ΚΡΗΤΗΣ - ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ
Λεωφ. Κνωσού, 714 09 Ηράκλειο. Τηλ: +30 2810393800, Fax +30 2810393881
It is well-known that a K-quasiconformal measure can distort Hausdorff dimension.
Astala famously proved sharp Hausdorff dimension distortion inequalities
for planar -quasiconformal mapping
: If
had H-dimension
, the
image has H-dimension at most
, where
. We answer in the
positive Astala's question if a set of zero Hausdorff
-measure is carried
into Hausdorff
-measure. The ingredients of the proof come from Astala's
original approach, geometric measure theory, and some new weighted norm inequalities
for Calderón-Zygmund singular integral operators which cannot
be deduced from the classical Muckenhoupt
theory.
Joint work with Ignacio Uriate-Tuero and Eric Sawyer.
http://fourier.math.uoc.gr/~ seminar