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