Linear functions and duality on the infinite polytorus

• Autores: Ole Fredrik Brevig
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 70, Fasc. 3, 2019, págs. 493-500
• Idioma: inglés
• DOI: 10.1007/s13348-019-00243-8
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• Resumen

  • 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.