This volume is based on lectures delivered at the international conference “New
trends in harmonic and complex analysis”, held May 7–12, 2007 in Voss, Norway,
and organized by the University of Bergen and the Norwegian University
of Science and Technology, Trondheim. It became the kick-off conference of the
European Science Foundation Networking Programme “Harmonic and complex
analysis and its applications” (2007–2012). The purpose of the Conference was to
bring together both experts and novices in analysis with experts in mathematical
physics, mechanics and adjacent areas of applied science and numerical analysis.
The participants presented their results and discussed further developments of
frontier research exploring the bridge between complex, real analysis, potential
theory, PDE and modern topics of fluid mechanics and mathematical physics.