Geometric and harmonic analysis for weights

Geometric and harmonic analysis for weights

Our research focuses on the study of geometric and analytical aspects of various classes of weight functions that are ubiquitous in harmonic analysis. The main goals of this project are to substantially improve some of the well-known fundamental norm inequalities for Muckenhoupt weights (the Reverse Hölder Inequality) and BMO functions (the John-Nirenberg estimate), to continue developing the theory of Békollé-Bonami weights in all dimensions, and to describe the geometry of the extension domains for both classes of weights. Our methods combine classical tools in harmonic and geometric analysis with more sophisticated probabilistic techniques that have been employed in the theory of Calderón-Zygmund operators in the setting of non-doubling measures, and in sharp maximal inequalities. The proposal is based at the Department of Mathematical Sciences (IMF), NTNU, Trondheim, Norway, with Karl-Mikael Perfekt as the supervisor of the fellowship. In addition to the research outcomes, the plan include lecturing and supervising activities, dissemination of the results in conferences, and participation in outreach activities organized by the NTNU. The research will be carried out within the research group "Fourier Analysis and Multiplicative Analysis", at the same department, whose Principal Investigator is Kristian Seip.