Resumen de Linear functions and duality on the infinite polytorus

Ole Fredrik Brevig

• We consider the following question: are there exponents 2 < p < q such that the Riesz projection is bounded from L^q to L^p on the infinite polytorus? We are unable to answer the question, but our counter-example improves a result of Marzo and Seip by demonstrating that the Riesz projection is unbounded from L^\infty to L^p if p\ge 3.31138. A similar result can be extracted for any q>2. Our approach is based on duality arguments and a detailed study of linear functions. Some related results are also presented.