Topic: Some harmonic analysis in mixed Lebesgue spaces

Abstract: Mixed Lebesgue spaces have attracted interests in harmonic analysis since the early 60’s. These spaces naturally appear when considering functions with different quantitative behavior on different sets of variables on which they depend. For example, this is the case when considering functions with physical relevance and that depend on both time and spaces variables. Mixed Lebesgue spaces can also be seen as vector-valued Lebesgue spaces. Using such point of view we will revisit some results in the literature and present some new ones about Leibniz’s rule for fractional derivatives, sampling, Calderon’s reproducing formula, and wavelets in the context of mixed norms. The new results in this lecture are joint work with Erika Ward.