Several results in classical and modern harmonic analysis in mixed Lebesgue spaces (Harmonic Analysis and Nonlinear Partial Differential Equations)

Abstract

Mixed Lebesgue spaces have attracted the interest of harmonic analysts since the early sixties. These spaces naturally appear when considering functions with different quantitive behavior on different sets of variables on which they depend. For example, this is the case when studying functions with physical relevance like the solutions of partial differential equations with time and space dependence. Mixed Lebesgue spaces can also be seen as vector-valued Lebesgue spaces. Using this point of view we revisit some classical results in the literature and survey newer ones about Leibniz's rule for fractional derivatives, bilinear null forms, sampling, Calderóns reproducing formula, and wavelets in the context of mixed norms.