The Hilbert transform, rearrangements, and logarithmic determinants
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
math.CA↗
arXiv subjects
V. Matsaev
Publications and source records attributed to V. Matsaev.
Variations on the theme of Marcinkiewicz' inequality
We present a new approach to the Marcinkiewicz interpolation inequality for the distribution function of the Hilbert transform, and prove an "abstract" version of this inequality. The approach uses "logarithmic determinants" and new estimates of canonical products of genus one.
math.CV↗